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Sang-Yoon Kim

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Papers by Sang-Yoon Kim

Effect of inhibitory spike-timing-dependent plasticity on fast sparsely synchronized rhythms in a small-world neuronal network

Neural Networks, 2018

We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Iz... more We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity D. We employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)]. Depending on values of D, population-averaged values of saturated synaptic inhibition strengths are potentiated [longterm potentiation (LTP)] or depressed [long-term depression (LTD)] in comparison with the initial mean value, and dispersions from the mean values of LTP/LTD are much increased when compared with the initial dispersion, independently of D. In most cases of LTD where the effect of mean LTD is dominant in comparison with the effect of dispersion, good synchronization (with higher spiking measure) is found to get better via LTD, while bad synchronization (with lower spiking measure) is found to get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre-and the post-synaptic spike times. Furthermore, we also investigate the effects of network architecture on FSS by changing the rewiring probability p of the SWN in the presence of iSTDP.

Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity

Neural Networks, 2018

We consider the Watts-Strogatz small-world network (SWN) consisting of subthreshold neurons which... more We consider the Watts-Strogatz small-world network (SWN) consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities. Here, we investigate the effect of additive STDP on the SSS by varying the noise intensity. Occurrence of a "Matthew" effect in synaptic plasticity is found due to a positive feedback process. As a result, good synchronization gets better via long-term potentiation of synaptic strengths, while bad synchronization gets worse via long-term depression. Emergences of long-term potentiation and long-term depression of synaptic strengths are intensively investigated via microscopic studies based on the pair-correlations between the pre-and the post-synaptic IISRs (instantaneous individual spike rates) as well as the distributions of time delays between the pre-and the post-synaptic spike times. Furthermore, the effects of multiplicative STDP (which depends on states) on the SSS are studied and discussed in comparison with the case of additive STDP (independent of states). These effects of STDP on the SSS in the SWN are also compared with those in the regular lattice and the random graph.

Effect of Interpopulation Spike-Timing-Dependent Plasticity on Synchronized Rhythms in Neuronal Networks with Inhibitory and Excitatory Populations

We consider a two-population network consisting of both inhibitory (I) interneurons and excitator... more We consider a two-population network consisting of both inhibitory (I) interneurons and excitatory (E) pyramidal cells. This I-E neuronal network has adaptive dynamic I to E and E to I interpopulation synaptic strengths, governed by interpopulation spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast sparsely synchronized rhythms, related to diverse cognitive functions, were found to appear in a range of noise intensityDfor static synaptic strengths. Here, by varyingD, we investigate the effect of interpopulation STDPs on fast sparsely synchronized rhythms that emerge in both the I- and the E-populations. Depending on values ofD, long-term potentiation (LTP) and long-term depression (LTD) for population-averaged values of saturated interpopulation synaptic strengths are found to occur. Then, the degree of fast sparse synchronization varies due to effects of LTP and LTD. In a broad region of intermediateD, the degree of good synchronization (with higher syn...

Thermodynamic order parameters and statistical–mechanical measures for characterization of the burst and spike synchronizations of bursting neurons

Physica A: Statistical Mechanics and its Applications, 2015

We are interested in characterization of population synchronization of bursting neurons which exh... more We are interested in characterization of population synchronization of bursting neurons which exhibit both the slow bursting and the fast spiking timescales, in contrast to spiking neurons. Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments. The instantaneous population firing rate (IPFR) R(t), which may be directly obtained from the raster plot of spikes, is often used as a realistic collective quantity describing population behaviors in both the computational and the experimental neuroscience. For the case of spiking neurons, realistic thermodynamic order parameter and statistical-mechanical spiking measure, based on R(t), were introduced in our recent work to make practical characterization of spike synchronization. Here, we separate the slow bursting and the fast spiking timescales via frequency filtering, and extend the thermodynamic order parameter and the statistical-mechanical measure to the case of bursting neurons. Consequently, it is shown in explicit examples that both the order parameters and the statistical-mechanical measures may be effectively used to characterize the burst and spike synchronizations of bursting neurons.

Emergence of ultrafast sparsely synchronized rhythms and their responses to external stimuli in an inhomogeneous small-world complex neuronal network

Neural Networks, 2017

h i g h l i g h t s • An inhomogeneous small-work neuronal network, composed of long-range (LR) a... more h i g h l i g h t s • An inhomogeneous small-work neuronal network, composed of long-range (LR) and short-range (SR) interneurons, is considered. • Distribution of betweenness centralities, representing the effectiveness for transfer of stimulation effect, is inhomogeneous. • Betweenness centralities of LR interneurons are much larger than those of SR interneurons. • Effects of network architecture on emergence of sparsely synchronized rhythms are studied. • Dynamical responses to external time-periodic stimuli are investigated in connection with betweenness centralities of stimulated interneurons.

Dynamical responses to external stimuli for both cases of excitatory and inhibitory synchronization in a complex neuronal network

Cognitive Neurodynamics, 2017

Your article is protected by copyright and all rights are held exclusively by Springer Science +B... more Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media Dordrecht. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons

Neural networks : the official journal of the International Neural Network Society, 2016

We investigate the effect of network architecture on burst and spike synchronization in a directe... more We investigate the effect of network architecture on burst and spike synchronization in a directed scale-free network (SFN) of bursting neurons, evolved via two independent α- and β-processes. The α-process corresponds to a directed version of the Barabási-Albert SFN model with growth and preferential attachment, while for the β-process only preferential attachments between pre-existing nodes are made without addition of new nodes. We first consider the "pure" α-process of symmetric preferential attachment (with the same in- and out-degrees), and study emergence of burst and spike synchronization by varying the coupling strength J and the noise intensity D for a fixed attachment degree. Characterizations of burst and spike synchronization are also made by employing realistic order parameters and statistical-mechanical measures. Next, we choose appropriate values of J and D where only burst synchronization occurs, and investigate the effect of the scale-free connectivity on...

Effect of intermodular connection on fast sparse synchronization in clustered small-world neural networks

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We consider a clustered network with small-world subnetworks of inhibitory fast spiking interneur... more We consider a clustered network with small-world subnetworks of inhibitory fast spiking interneurons and investigate the effect of intermodular connection on the emergence of fast sparsely synchronized rhythms by varying both the intermodular coupling strength J_{inter} and the average number of intermodular links per interneuron M_{syn}^{(inter)}. In contrast to the case of nonclustered networks, two kinds of sparsely synchronized states such as modular and global synchronization are found. For the case of modular sparse synchronization, the population behavior reveals the modular structure, because the intramodular dynamics of subnetworks make some mismatching. On the other hand, in the case of global sparse synchronization, the population behavior is globally identical, independently of the cluster structure, because the intramodular dynamics of subnetworks make perfect matching. We introduce a realistic cross-correlation modularity measure, representing the matching degree betwe...

Bifurcations in a Horizontally Driven Pendulum

Journal- Korean Physical Society

We consider a forced pendulum with a horizontally oscillating suspension point. Bifurcations asso... more We consider a forced pendulum with a horizontally oscillating suspension point. Bifurcations associated with stability of the symmetric period-1 orbit (SPO), arising from the "unforced" stationary point, are investigated in details by varying the two parameters A (the normalized driving amplitude) and Ω (the normalized natural frequency). We thus obtain the phase diagram showing the bifurcation curves of the SPO in the Ω − A plane through numerical calculations of the Floquet (stability) multipliers and winding numbers. We note that a specific substructure in the bifurcation set of the SPO recurs in the parameter plane.

Mechanism for New Boundary Crises in Quasiperiodically Forced Systems

Journal- Korean Physical Society

As a representative model for the Poincaré map of quasiperiodically forced oscillators, we consid... more As a representative model for the Poincaré map of quasiperiodically forced oscillators, we consider the quasiperiodically forced Hénon map and investigate the mechanism for boundary crises. Using rational approximations to quasiperiodic forcing, we show that a new type of boundary crisis occurs for a nonchaotic attractor (smooth torus or strange nonchaotic attractor), as well as a chaotic attractor, through a collision with an invariant "ring-shaped" unstable set which has no counterpart in the unforced case. This new boundary crisis is in contrast to the "standard" boundary crisis that occurs via a collision with smooth unstable torus.

Fast sparsely synchronized brain rhythms in a scale-free neural network

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We consider a directed version of the Barabási-Albert scale-free network model with symmetric pre... more We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D. For small D, full synchronization with the same population-rhythm frequency f_{p} and mean firing rate (MFR) f_{i} of individual neurons occurs, while for large D partial synchronization with f_{p}>〈f_{i}〉 (〈f_{i}〉: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of f_{p}>4〈f_{i}〉 is referred to as sparse synchronizati...

Frequency-domain order parameters for the burst and spike synchronization transitions of bursting neurons

Cognitive neurodynamics, 2015

We are interested in characterization of synchronization transitions of bursting neurons in the f... more We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) [Formula: see text], which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on [Formula: see text], was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR [Formula: see text] of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR [Formula: see text] into the instantaneous population bursting rate [Formula: see text] (describing the bursting behavior) and the instantaneous population spike rate [Formula: see text] (describing the spi...

Dynamic stabilization in the double-well Duffing oscillator

Physical Review E, 2000

Bifurcations associated with stability of the saddle fixed point of the Poincaré map, arising fro... more Bifurcations associated with stability of the saddle fixed point of the Poincaré map, arising from the unstable equilibrium point of the potential, are investigated in a forced Duffing oscillator with a double-well potential. One interesting behavior is the dynamic stabilization of the saddle fixed point. When the driving amplitude is increased through a threshold value, the saddle fixed point becomes stabilized via a pitchfork bifurcation. We note that this dynamic stabilization is similar to that of the inverted pendulum with a vertically oscillating suspension point. After the dynamic stabilization, the double-well Duffing oscillator behaves as the single-well Duffing oscillator, because the effect of the central potential barrier on the dynamics of the system becomes negligible.

Period doublings in coupled parametrically forced damped pendulums

Physical Review E, 1996

We study period doublings in N (N = 2, 3, 4,. . .) coupled parametrically forced damped pendulums... more We study period doublings in N (N = 2, 3, 4,. . .) coupled parametrically forced damped pendulums by varying A (the amplitude of the external driving force) and c (the strength of coupling). With increasing A, the stationary point undergoes multiple period-doubling transitions to chaos. We first investigate the two-coupled case with N = 2. For each period-doubling transition to chaos, the critical set consists of an infinity of critical line segments and the zero-coupling critical point lying on the line A = A * i in the A − c plane, where A * i is the ith transition point for the uncoupled case. We find three kinds of critical behaviors, depending on the position on the critical set. They are the same as those for the coupled one-dimensional maps. Finally, the results of the N = 2 case are extended to many-coupled cases with N ≥ 3, in which the critical behaviors depend on the range of coupling.

Multiple transitions to chaos in a damped parametrically forced pendulum

Physical Review E, 1996

We study bifurcations associated with stability of the lowest stationary point (SP) of a damped p... more We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying ω 0 (the natural frequency of the pendulum) and A (the amplitude of the external driving force). As A is increased, the SP will restabilize after its instability, destabilize again, and so ad infinitum for any given ω 0. Its destabilizations (restabilizations) occur via alternating supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork bifurcations, except the first destabilization at which a supercritical or subcritical bifurcation takes place depending on the value of ω 0. For each case of the supercritical destabilizations, an infinite sequence of PDB's follows and leads to chaos. Consequently, an infinite series of period-doubling transitions to chaos appears with increasing A. The critical behaviors at the transition points are also discussed.

Coupling-Induced Spiking Coherence in Coupled Subthreshold Neurons

International Journal of Modern Physics B, 2009

We consider a large ensemble of globally coupled subthreshold Morris–Lecar neurons. We numericall... more We consider a large ensemble of globally coupled subthreshold Morris–Lecar neurons. We numerically investigate collective coherence of noise-induced spikings by varying the coupling strength J. As J passes a lower threshold, a transition to collective spiking coherence, which is described in terms of an order parameter, occurs because the coupling stimulates coherence between noise-induced spikings. However, when passing a higher threshold, the coupling induces oscillator death (i.e., quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state. Through competition of these two different roles of coupling, coupling-induced spiking coherence is found to occur in a large range of intermediate coupling strength. The degree of spiking coherence is well-characterized in terms of a coherence measure reflecting the degree of "resemblance" of the global potential to the local potential.

Stochastic Spiking Coherence in Coupled Subthreshold Morris-Lecar Neurons

International Journal of Modern Physics B, 2009

We consider a large population of globally coupled subthreshold Morris-Lecar neurons. By varying ... more We consider a large population of globally coupled subthreshold Morris-Lecar neurons. By varying the noise intensity D, we numerically investigate stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings). As D passes a lower threshold, a transition from an incoherent to a coherent state occurs because of a constructive role of noise to stimulate coherence between noise-induced spikings. However, when passing a higher threshold of D, another transition from a coherent to an incoherent state takes place due to a destructive role of noise to spoil the spiking coherence. Such an incoherence-coherence-incoherence transition is well-described in terms of the order parameter which is just the mean square deviation of the global potential. In the coherent regime, we also characterize the degree of stochastic spiking coherence by using a coherence measure which reflects the degree of "resemblance" of the global potential to the local potential...

Effect of small-world connectivity on fast sparsely synchronized cortical rhythms

Physica A: Statistical Mechanics and its Applications, 2015

Fast cortical rhythms with stochastic and intermittent neural discharges have been observed in el... more Fast cortical rhythms with stochastic and intermittent neural discharges have been observed in electric recordings of brain activity. For these fast sparsely synchronized oscillations, individual neurons fire spikings irregularly and sparsely as Geiger counters, in contrast to fully synchronized oscillations where individual neurons exhibit regular firings like clocks. We study the effect of network architecture on these fast sparsely synchronized rhythms in an inhibitory population of suprathreshold fast spiking (FS) Izhikevich interneurons (which fire spontaneously without noise). We first employ the conventional Erdös-Renyi random

Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

Cognitive Neurodynamics, 2014

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding... more We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the J-D plane (J: synaptic inhibition strength and D: noise intensity). As the rewiring probability p is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the J-D plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.

Interior crises in quasiperiodically forced period-doubling systems

Physics Letters A, 2006

As a representative model for quasiperiodically forced period-doubling systems, we consider the q... more As a representative model for quasiperiodically forced period-doubling systems, we consider the quasiperiodically forced logistic map, and investigate the dynamical mechanism for the interior crises. For small quasiperiodic forcing ε, a chaotic attractor abruptly widens via a "standard" interior crisis when it collides with a smooth unstable torus. However, as ε passes a threshold value, the smooth unstable torus loses its accessibility from the interior of the basin of the attractor. For this case, we use the rational approximation to the quasiperiodic forcing, and find that a nonstandard interior crisis occurs for a nonchaotic attractor (smooth torus or strange nonchaotic attractor) as well as a chaotic attractor when it collides with an invariant "ring-shaped" unstable set. Particularly, we note that a three-band smooth torus transforms into a single-band intermittent strange nonchaotic attractor through the nonstandard interior crisis. The intermittent strange nonchaotic attractor is also characterized in terms of the average interburst time and the local Lyapunov exponent.

Effect of inhibitory spike-timing-dependent plasticity on fast sparsely synchronized rhythms in a small-world neuronal network

Neural Networks, 2018

We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Iz... more We consider the Watts-Strogatz small-world network (SWN) consisting of inhibitory fast spiking Izhikevich interneurons. This inhibitory neuronal population has adaptive dynamic synaptic strengths governed by the inhibitory spike-timing-dependent plasticity (iSTDP). In previous works without iSTDP, fast sparsely synchronized rhythms, associated with diverse cognitive functions, were found to appear in a range of large noise intensities for fixed strong synaptic inhibition strengths. Here, we investigate the effect of iSTDP on fast sparse synchronization (FSS) by varying the noise intensity D. We employ an asymmetric anti-Hebbian time window for the iSTDP update rule [which is in contrast to the Hebbian time window for the excitatory STDP (eSTDP)]. Depending on values of D, population-averaged values of saturated synaptic inhibition strengths are potentiated [longterm potentiation (LTP)] or depressed [long-term depression (LTD)] in comparison with the initial mean value, and dispersions from the mean values of LTP/LTD are much increased when compared with the initial dispersion, independently of D. In most cases of LTD where the effect of mean LTD is dominant in comparison with the effect of dispersion, good synchronization (with higher spiking measure) is found to get better via LTD, while bad synchronization (with lower spiking measure) is found to get worse via LTP. This kind of Matthew effect in inhibitory synaptic plasticity is in contrast to that in excitatory synaptic plasticity where good (bad) synchronization gets better (worse) via LTP (LTD). Emergences of LTD and LTP of synaptic inhibition strengths are intensively investigated via a microscopic method based on the distributions of time delays between the pre-and the post-synaptic spike times. Furthermore, we also investigate the effects of network architecture on FSS by changing the rewiring probability p of the SWN in the presence of iSTDP.

Stochastic spike synchronization in a small-world neural network with spike-timing-dependent plasticity

Neural Networks, 2018

We consider the Watts-Strogatz small-world network (SWN) consisting of subthreshold neurons which... more We consider the Watts-Strogatz small-world network (SWN) consisting of subthreshold neurons which exhibit noise-induced spikings. This neuronal network has adaptive dynamic synaptic strengths governed by the spike-timing-dependent plasticity (STDP). In previous works without STDP, stochastic spike synchronization (SSS) between noise-induced spikings of subthreshold neurons was found to occur in a range of intermediate noise intensities. Here, we investigate the effect of additive STDP on the SSS by varying the noise intensity. Occurrence of a "Matthew" effect in synaptic plasticity is found due to a positive feedback process. As a result, good synchronization gets better via long-term potentiation of synaptic strengths, while bad synchronization gets worse via long-term depression. Emergences of long-term potentiation and long-term depression of synaptic strengths are intensively investigated via microscopic studies based on the pair-correlations between the pre-and the post-synaptic IISRs (instantaneous individual spike rates) as well as the distributions of time delays between the pre-and the post-synaptic spike times. Furthermore, the effects of multiplicative STDP (which depends on states) on the SSS are studied and discussed in comparison with the case of additive STDP (independent of states). These effects of STDP on the SSS in the SWN are also compared with those in the regular lattice and the random graph.

Effect of Interpopulation Spike-Timing-Dependent Plasticity on Synchronized Rhythms in Neuronal Networks with Inhibitory and Excitatory Populations

We consider a two-population network consisting of both inhibitory (I) interneurons and excitator... more We consider a two-population network consisting of both inhibitory (I) interneurons and excitatory (E) pyramidal cells. This I-E neuronal network has adaptive dynamic I to E and E to I interpopulation synaptic strengths, governed by interpopulation spike-timing-dependent plasticity (STDP). In previous works without STDPs, fast sparsely synchronized rhythms, related to diverse cognitive functions, were found to appear in a range of noise intensityDfor static synaptic strengths. Here, by varyingD, we investigate the effect of interpopulation STDPs on fast sparsely synchronized rhythms that emerge in both the I- and the E-populations. Depending on values ofD, long-term potentiation (LTP) and long-term depression (LTD) for population-averaged values of saturated interpopulation synaptic strengths are found to occur. Then, the degree of fast sparse synchronization varies due to effects of LTP and LTD. In a broad region of intermediateD, the degree of good synchronization (with higher syn...

Thermodynamic order parameters and statistical–mechanical measures for characterization of the burst and spike synchronizations of bursting neurons

Physica A: Statistical Mechanics and its Applications, 2015

We are interested in characterization of population synchronization of bursting neurons which exh... more We are interested in characterization of population synchronization of bursting neurons which exhibit both the slow bursting and the fast spiking timescales, in contrast to spiking neurons. Population synchronization may be well visualized in the raster plot of neural spikes which can be obtained in experiments. The instantaneous population firing rate (IPFR) R(t), which may be directly obtained from the raster plot of spikes, is often used as a realistic collective quantity describing population behaviors in both the computational and the experimental neuroscience. For the case of spiking neurons, realistic thermodynamic order parameter and statistical-mechanical spiking measure, based on R(t), were introduced in our recent work to make practical characterization of spike synchronization. Here, we separate the slow bursting and the fast spiking timescales via frequency filtering, and extend the thermodynamic order parameter and the statistical-mechanical measure to the case of bursting neurons. Consequently, it is shown in explicit examples that both the order parameters and the statistical-mechanical measures may be effectively used to characterize the burst and spike synchronizations of bursting neurons.

Emergence of ultrafast sparsely synchronized rhythms and their responses to external stimuli in an inhomogeneous small-world complex neuronal network

Neural Networks, 2017

h i g h l i g h t s • An inhomogeneous small-work neuronal network, composed of long-range (LR) a... more h i g h l i g h t s • An inhomogeneous small-work neuronal network, composed of long-range (LR) and short-range (SR) interneurons, is considered. • Distribution of betweenness centralities, representing the effectiveness for transfer of stimulation effect, is inhomogeneous. • Betweenness centralities of LR interneurons are much larger than those of SR interneurons. • Effects of network architecture on emergence of sparsely synchronized rhythms are studied. • Dynamical responses to external time-periodic stimuli are investigated in connection with betweenness centralities of stimulated interneurons.

Dynamical responses to external stimuli for both cases of excitatory and inhibitory synchronization in a complex neuronal network

Cognitive Neurodynamics, 2017

Your article is protected by copyright and all rights are held exclusively by Springer Science +B... more Your article is protected by copyright and all rights are held exclusively by Springer Science +Business Media Dordrecht. This e-offprint is for personal use only and shall not be selfarchived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may further deposit the accepted manuscript version in any repository, provided it is only made publicly available 12 months after official publication or later and provided acknowledgement is given to the original source of publication and a link is inserted to the published article on Springer's website. The link must be accompanied by the following text: "The final publication is available at link.springer.com".

Effect of network architecture on burst and spike synchronization in a scale-free network of bursting neurons

Neural networks : the official journal of the International Neural Network Society, 2016

We investigate the effect of network architecture on burst and spike synchronization in a directe... more We investigate the effect of network architecture on burst and spike synchronization in a directed scale-free network (SFN) of bursting neurons, evolved via two independent α- and β-processes. The α-process corresponds to a directed version of the Barabási-Albert SFN model with growth and preferential attachment, while for the β-process only preferential attachments between pre-existing nodes are made without addition of new nodes. We first consider the "pure" α-process of symmetric preferential attachment (with the same in- and out-degrees), and study emergence of burst and spike synchronization by varying the coupling strength J and the noise intensity D for a fixed attachment degree. Characterizations of burst and spike synchronization are also made by employing realistic order parameters and statistical-mechanical measures. Next, we choose appropriate values of J and D where only burst synchronization occurs, and investigate the effect of the scale-free connectivity on...

Effect of intermodular connection on fast sparse synchronization in clustered small-world neural networks

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We consider a clustered network with small-world subnetworks of inhibitory fast spiking interneur... more We consider a clustered network with small-world subnetworks of inhibitory fast spiking interneurons and investigate the effect of intermodular connection on the emergence of fast sparsely synchronized rhythms by varying both the intermodular coupling strength J_{inter} and the average number of intermodular links per interneuron M_{syn}^{(inter)}. In contrast to the case of nonclustered networks, two kinds of sparsely synchronized states such as modular and global synchronization are found. For the case of modular sparse synchronization, the population behavior reveals the modular structure, because the intramodular dynamics of subnetworks make some mismatching. On the other hand, in the case of global sparse synchronization, the population behavior is globally identical, independently of the cluster structure, because the intramodular dynamics of subnetworks make perfect matching. We introduce a realistic cross-correlation modularity measure, representing the matching degree betwe...

Bifurcations in a Horizontally Driven Pendulum

Journal- Korean Physical Society

We consider a forced pendulum with a horizontally oscillating suspension point. Bifurcations asso... more We consider a forced pendulum with a horizontally oscillating suspension point. Bifurcations associated with stability of the symmetric period-1 orbit (SPO), arising from the "unforced" stationary point, are investigated in details by varying the two parameters A (the normalized driving amplitude) and Ω (the normalized natural frequency). We thus obtain the phase diagram showing the bifurcation curves of the SPO in the Ω − A plane through numerical calculations of the Floquet (stability) multipliers and winding numbers. We note that a specific substructure in the bifurcation set of the SPO recurs in the parameter plane.

Mechanism for New Boundary Crises in Quasiperiodically Forced Systems

Journal- Korean Physical Society

As a representative model for the Poincaré map of quasiperiodically forced oscillators, we consid... more As a representative model for the Poincaré map of quasiperiodically forced oscillators, we consider the quasiperiodically forced Hénon map and investigate the mechanism for boundary crises. Using rational approximations to quasiperiodic forcing, we show that a new type of boundary crisis occurs for a nonchaotic attractor (smooth torus or strange nonchaotic attractor), as well as a chaotic attractor, through a collision with an invariant "ring-shaped" unstable set which has no counterpart in the unforced case. This new boundary crisis is in contrast to the "standard" boundary crisis that occurs via a collision with smooth unstable torus.

Fast sparsely synchronized brain rhythms in a scale-free neural network

Physical review. E, Statistical, nonlinear, and soft matter physics, 2015

We consider a directed version of the Barabási-Albert scale-free network model with symmetric pre... more We consider a directed version of the Barabási-Albert scale-free network model with symmetric preferential attachment with the same in- and out-degrees and study the emergence of sparsely synchronized rhythms for a fixed attachment degree in an inhibitory population of fast-spiking Izhikevich interneurons. Fast sparsely synchronized rhythms with stochastic and intermittent neuronal discharges are found to appear for large values of J (synaptic inhibition strength) and D (noise intensity). For an intensive study we fix J at a sufficiently large value and investigate the population states by increasing D. For small D, full synchronization with the same population-rhythm frequency f_{p} and mean firing rate (MFR) f_{i} of individual neurons occurs, while for large D partial synchronization with f_{p}>〈f_{i}〉 (〈f_{i}〉: ensemble-averaged MFR) appears due to intermittent discharge of individual neurons; in particular, the case of f_{p}>4〈f_{i}〉 is referred to as sparse synchronizati...

Frequency-domain order parameters for the burst and spike synchronization transitions of bursting neurons

Cognitive neurodynamics, 2015

We are interested in characterization of synchronization transitions of bursting neurons in the f... more We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) [Formula: see text], which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on [Formula: see text], was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR [Formula: see text] of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR [Formula: see text] into the instantaneous population bursting rate [Formula: see text] (describing the bursting behavior) and the instantaneous population spike rate [Formula: see text] (describing the spi...

Dynamic stabilization in the double-well Duffing oscillator

Physical Review E, 2000

Bifurcations associated with stability of the saddle fixed point of the Poincaré map, arising fro... more Bifurcations associated with stability of the saddle fixed point of the Poincaré map, arising from the unstable equilibrium point of the potential, are investigated in a forced Duffing oscillator with a double-well potential. One interesting behavior is the dynamic stabilization of the saddle fixed point. When the driving amplitude is increased through a threshold value, the saddle fixed point becomes stabilized via a pitchfork bifurcation. We note that this dynamic stabilization is similar to that of the inverted pendulum with a vertically oscillating suspension point. After the dynamic stabilization, the double-well Duffing oscillator behaves as the single-well Duffing oscillator, because the effect of the central potential barrier on the dynamics of the system becomes negligible.

Period doublings in coupled parametrically forced damped pendulums

Physical Review E, 1996

We study period doublings in N (N = 2, 3, 4,. . .) coupled parametrically forced damped pendulums... more We study period doublings in N (N = 2, 3, 4,. . .) coupled parametrically forced damped pendulums by varying A (the amplitude of the external driving force) and c (the strength of coupling). With increasing A, the stationary point undergoes multiple period-doubling transitions to chaos. We first investigate the two-coupled case with N = 2. For each period-doubling transition to chaos, the critical set consists of an infinity of critical line segments and the zero-coupling critical point lying on the line A = A * i in the A − c plane, where A * i is the ith transition point for the uncoupled case. We find three kinds of critical behaviors, depending on the position on the critical set. They are the same as those for the coupled one-dimensional maps. Finally, the results of the N = 2 case are extended to many-coupled cases with N ≥ 3, in which the critical behaviors depend on the range of coupling.

Multiple transitions to chaos in a damped parametrically forced pendulum

Physical Review E, 1996

We study bifurcations associated with stability of the lowest stationary point (SP) of a damped p... more We study bifurcations associated with stability of the lowest stationary point (SP) of a damped parametrically forced pendulum by varying ω 0 (the natural frequency of the pendulum) and A (the amplitude of the external driving force). As A is increased, the SP will restabilize after its instability, destabilize again, and so ad infinitum for any given ω 0. Its destabilizations (restabilizations) occur via alternating supercritical (subcritical) period-doubling bifurcations (PDB's) and pitchfork bifurcations, except the first destabilization at which a supercritical or subcritical bifurcation takes place depending on the value of ω 0. For each case of the supercritical destabilizations, an infinite sequence of PDB's follows and leads to chaos. Consequently, an infinite series of period-doubling transitions to chaos appears with increasing A. The critical behaviors at the transition points are also discussed.

Coupling-Induced Spiking Coherence in Coupled Subthreshold Neurons

International Journal of Modern Physics B, 2009

We consider a large ensemble of globally coupled subthreshold Morris–Lecar neurons. We numericall... more We consider a large ensemble of globally coupled subthreshold Morris–Lecar neurons. We numerically investigate collective coherence of noise-induced spikings by varying the coupling strength J. As J passes a lower threshold, a transition to collective spiking coherence, which is described in terms of an order parameter, occurs because the coupling stimulates coherence between noise-induced spikings. However, when passing a higher threshold, the coupling induces oscillator death (i.e., quenching of noise-induced spikings) because each neuron is attracted to a noisy equilibrium state. Through competition of these two different roles of coupling, coupling-induced spiking coherence is found to occur in a large range of intermediate coupling strength. The degree of spiking coherence is well-characterized in terms of a coherence measure reflecting the degree of "resemblance" of the global potential to the local potential.

Stochastic Spiking Coherence in Coupled Subthreshold Morris-Lecar Neurons

International Journal of Modern Physics B, 2009

We consider a large population of globally coupled subthreshold Morris-Lecar neurons. By varying ... more We consider a large population of globally coupled subthreshold Morris-Lecar neurons. By varying the noise intensity D, we numerically investigate stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings). As D passes a lower threshold, a transition from an incoherent to a coherent state occurs because of a constructive role of noise to stimulate coherence between noise-induced spikings. However, when passing a higher threshold of D, another transition from a coherent to an incoherent state takes place due to a destructive role of noise to spoil the spiking coherence. Such an incoherence-coherence-incoherence transition is well-described in terms of the order parameter which is just the mean square deviation of the global potential. In the coherent regime, we also characterize the degree of stochastic spiking coherence by using a coherence measure which reflects the degree of "resemblance" of the global potential to the local potential...

Effect of small-world connectivity on fast sparsely synchronized cortical rhythms

Physica A: Statistical Mechanics and its Applications, 2015

Fast cortical rhythms with stochastic and intermittent neural discharges have been observed in el... more Fast cortical rhythms with stochastic and intermittent neural discharges have been observed in electric recordings of brain activity. For these fast sparsely synchronized oscillations, individual neurons fire spikings irregularly and sparsely as Geiger counters, in contrast to fully synchronized oscillations where individual neurons exhibit regular firings like clocks. We study the effect of network architecture on these fast sparsely synchronized rhythms in an inhibitory population of suprathreshold fast spiking (FS) Izhikevich interneurons (which fire spontaneously without noise). We first employ the conventional Erdös-Renyi random

Noise-induced burst and spike synchronizations in an inhibitory small-world network of subthreshold bursting neurons

Cognitive Neurodynamics, 2014

We are interested in noise-induced firings of subthreshold neurons which may be used for encoding... more We are interested in noise-induced firings of subthreshold neurons which may be used for encoding environmental stimuli. Noise-induced population synchronization was previously studied only for the case of global coupling, unlike the case of subthreshold spiking neurons. Hence, we investigate the effect of complex network architecture on noise-induced synchronization in an inhibitory population of subthreshold bursting Hindmarsh-Rose neurons. For modeling complex synaptic connectivity, we consider the Watts-Strogatz small-world network which interpolates between regular lattice and random network via rewiring, and investigate the effect of small-world connectivity on emergence of noise-induced population synchronization. Thus, noise-induced burst synchronization (synchrony on the slow bursting time scale) and spike synchronization (synchrony on the fast spike time scale) are found to appear in a synchronized region of the J-D plane (J: synaptic inhibition strength and D: noise intensity). As the rewiring probability p is decreased from 1 (random network) to 0 (regular lattice), the region of spike synchronization shrinks rapidly in the J-D plane, while the region of the burst synchronization decreases slowly. We separate the slow bursting and the fast spiking time scales via frequency filtering, and characterize the noise-induced burst and spike synchronizations by employing realistic order parameters and statistical-mechanical measures introduced in our recent work. Thus, the bursting and spiking thresholds for the burst and spike synchronization transitions are determined in terms of the bursting and spiking order parameters, respectively. Furthermore, we also measure the degrees of burst and spike synchronizations in terms of the statistical-mechanical bursting and spiking measures, respectively.

Interior crises in quasiperiodically forced period-doubling systems

Physics Letters A, 2006

As a representative model for quasiperiodically forced period-doubling systems, we consider the q... more As a representative model for quasiperiodically forced period-doubling systems, we consider the quasiperiodically forced logistic map, and investigate the dynamical mechanism for the interior crises. For small quasiperiodic forcing ε, a chaotic attractor abruptly widens via a "standard" interior crisis when it collides with a smooth unstable torus. However, as ε passes a threshold value, the smooth unstable torus loses its accessibility from the interior of the basin of the attractor. For this case, we use the rational approximation to the quasiperiodic forcing, and find that a nonstandard interior crisis occurs for a nonchaotic attractor (smooth torus or strange nonchaotic attractor) as well as a chaotic attractor when it collides with an invariant "ring-shaped" unstable set. Particularly, we note that a three-band smooth torus transforms into a single-band intermittent strange nonchaotic attractor through the nonstandard interior crisis. The intermittent strange nonchaotic attractor is also characterized in terms of the average interburst time and the local Lyapunov exponent.