International Journal of Social Sciences and Education Research
The aim of the study is to understand how the Turkish society evaluates the transition to distanc... more The aim of the study is to understand how the Turkish society evaluates the transition to distance education during the Covid-19 pandemic process by making sentiment analysis over Twitter posts. Hence, 28 prominent education-related tags were determined between 16.03.2020 - 17.05.2021. The data set was created by obtaining 8545 tweets in Turkish via the Twitter API. In addition, it was evaluated whether the number of cases reported daily by the authorities in the relevant period affected the shares positively or negatively. Finally, the most repeated words were evaluated to establish the most repetitive explanations. As a result, it was determined that the tweets related to distance education were in parallel with the increase in the number of cases and positive sharing due to health-related concerns.
In this study we analyze the Matinyan-Yang-Mills-Higgs (MYMH) system, based on semiclassical solu... more In this study we analyze the Matinyan-Yang-Mills-Higgs (MYMH) system, based on semiclassical solutions to a Yang-Mills model, using Poincaré surfaces of section and the method of averaging. To investigate the possible chaotic behavior for the system, we simulate the trajectories of the system and calculate the Lyapunov exponents. We observe that the system displays weakly chaotic behavior. We search for the existence of approximately conserved quantities for the system using the method of averaging. In this way, we show the existence of four fixed points where period orbits exist.
AJIT-e Online Academic Journal of Information Technology, 2019
Artificial neural networks are commonly accepted as a very successful tool for global function ap... more Artificial neural networks are commonly accepted as a very successful tool for global function approximation. Because of this reason, they are considered as a good approach to forecasting chaotic time series in many studies. For a given time series, the Lyapunov exponent is a good parameter to characterize the series as chaotic or not. In this study, we use three different neural network architectures to test capabilities of the neural network in forecasting time series generated from different dynamical systems. In addition to forecasting time series, using the feedforward neural network with single hidden layer, Lyapunov exponents of the studied systems are forecasted.
The Matinyan Yang Mills Higgs System (abbreviated MYMH), a generalization of the truncations of t... more The Matinyan Yang Mills Higgs System (abbreviated MYMH), a generalization of the truncations of the Toda Lattice, is a classical Hamiltonian system given below. It is well known that the Toda lattice is, while its truncations are not integrable [1]. Approximate integrals for the Toda system have been constructed. The present Hamiltonian has similar algebraic terms with somewhat different coefficients than the Toda truncations. The MYMH system has been used for modelling the suppression of chaotic behavior in the classical Yang Mills system. [2] This has become necessary in light of our recent understanding on the stability of the universe and the mechanism for the onset of instability. In recent work, this analysis was done by numerical simulation. In this study, we present results for analyzing the possible candidates for approximately conserved quantities (approximate invariants) in light of our work on the Toda truncations. One possible approach is to start from the basic second ...
Several modern predator prey like systems as well as a number of simple low dimensional chaotic s... more Several modern predator prey like systems as well as a number of simple low dimensional chaotic systems involve discontinuous functions. This causes difficulties in simulating such systems in order to obtain characteristics such as stationary points, local and structural stability, Lyapunov Exponents or limit cycles. These parameters are very important in understanding the models. The distinction between differential equations and discretized maps is also of interest, particularly in two dimensional systems. In this work, we propose to replace discontinuous functions by continuous functions that approximate them in order to facilitate the analysis. For example, the step function can be replaced by an inverse tangent or hyperbolic tangent.
1 Department of Physics and Department of Information Systems and Technologies, Yeditepe Universi... more 1 Department of Physics and Department of Information Systems and Technologies, Yeditepe University, Ataşehir, Istanbul, Turkey(E-mail: [email protected]) 2 Department of Information Systems and Technologies, Yeditepe University,Ataşehir,Istanbul, Turkey and The Institute for Graduate Studies in Sciences and Engineering, Yeditepe University, İstanbul Turkey. (E-mail: [email protected]) Abstract: The Sprott C and D systems are among the three variable simplest chaotic systems with resonant normal form characteristics and serve as possible candidates for demonstrating Hopf Bifurcation. Investigation of Sprott systems for deriving jerky Dynamics has also become of interest. The jerky dynamics has been analyzed with approximating discontinuities with a continuous function. In this work, we will use slightly generalized forms of these two Sprott systems, derive jerky systems compatible with them, analyze their transition to chaotic behavior and their attractors using ou...
In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modif... more In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final ...
11th Chaotic Modeling and Simulation International Conference
Many models of physical systems involving electronic circuit elements [6], population dynamics [5... more Many models of physical systems involving electronic circuit elements [6], population dynamics [5] involve evolution equations with discontinuities. The key to understand such systems is to hope that the discontinuity does not adversely affect the integration process. There are also three variable chaotic dynamical system examples, such as the Sprott systems for deriving jerky dynamics that have also become of interest [10]. In order to calculate dynamical invariants in chaotic systems such as characteristic exponents and fractal dimensions we often need to find the Jacobian; this often requires attempting to differentiate discontinuous functions. Therefore finding a suitable continuous approximation to the discontinuities becomes important. In previous communications, two example systems had been used with two parametrizations for approximating discontinuous functions with continuous ones, one of which is the same as that used in the literature. In this work, we will use further examples to optimize the parameters of the continuous approximation to discontinuities using different examples in order to test the degree of applicability of this approach. Where possible, the invariants calculated by this method will be compared to the corresponding invariants calculated from its time series.
International Journal of Social Sciences and Education Research
The aim of the study is to understand how the Turkish society evaluates the transition to distanc... more The aim of the study is to understand how the Turkish society evaluates the transition to distance education during the Covid-19 pandemic process by making sentiment analysis over Twitter posts. Hence, 28 prominent education-related tags were determined between 16.03.2020 - 17.05.2021. The data set was created by obtaining 8545 tweets in Turkish via the Twitter API. In addition, it was evaluated whether the number of cases reported daily by the authorities in the relevant period affected the shares positively or negatively. Finally, the most repeated words were evaluated to establish the most repetitive explanations. As a result, it was determined that the tweets related to distance education were in parallel with the increase in the number of cases and positive sharing due to health-related concerns.
In this study we analyze the Matinyan-Yang-Mills-Higgs (MYMH) system, based on semiclassical solu... more In this study we analyze the Matinyan-Yang-Mills-Higgs (MYMH) system, based on semiclassical solutions to a Yang-Mills model, using Poincaré surfaces of section and the method of averaging. To investigate the possible chaotic behavior for the system, we simulate the trajectories of the system and calculate the Lyapunov exponents. We observe that the system displays weakly chaotic behavior. We search for the existence of approximately conserved quantities for the system using the method of averaging. In this way, we show the existence of four fixed points where period orbits exist.
AJIT-e Online Academic Journal of Information Technology, 2019
Artificial neural networks are commonly accepted as a very successful tool for global function ap... more Artificial neural networks are commonly accepted as a very successful tool for global function approximation. Because of this reason, they are considered as a good approach to forecasting chaotic time series in many studies. For a given time series, the Lyapunov exponent is a good parameter to characterize the series as chaotic or not. In this study, we use three different neural network architectures to test capabilities of the neural network in forecasting time series generated from different dynamical systems. In addition to forecasting time series, using the feedforward neural network with single hidden layer, Lyapunov exponents of the studied systems are forecasted.
The Matinyan Yang Mills Higgs System (abbreviated MYMH), a generalization of the truncations of t... more The Matinyan Yang Mills Higgs System (abbreviated MYMH), a generalization of the truncations of the Toda Lattice, is a classical Hamiltonian system given below. It is well known that the Toda lattice is, while its truncations are not integrable [1]. Approximate integrals for the Toda system have been constructed. The present Hamiltonian has similar algebraic terms with somewhat different coefficients than the Toda truncations. The MYMH system has been used for modelling the suppression of chaotic behavior in the classical Yang Mills system. [2] This has become necessary in light of our recent understanding on the stability of the universe and the mechanism for the onset of instability. In recent work, this analysis was done by numerical simulation. In this study, we present results for analyzing the possible candidates for approximately conserved quantities (approximate invariants) in light of our work on the Toda truncations. One possible approach is to start from the basic second ...
Several modern predator prey like systems as well as a number of simple low dimensional chaotic s... more Several modern predator prey like systems as well as a number of simple low dimensional chaotic systems involve discontinuous functions. This causes difficulties in simulating such systems in order to obtain characteristics such as stationary points, local and structural stability, Lyapunov Exponents or limit cycles. These parameters are very important in understanding the models. The distinction between differential equations and discretized maps is also of interest, particularly in two dimensional systems. In this work, we propose to replace discontinuous functions by continuous functions that approximate them in order to facilitate the analysis. For example, the step function can be replaced by an inverse tangent or hyperbolic tangent.
1 Department of Physics and Department of Information Systems and Technologies, Yeditepe Universi... more 1 Department of Physics and Department of Information Systems and Technologies, Yeditepe University, Ataşehir, Istanbul, Turkey(E-mail: [email protected]) 2 Department of Information Systems and Technologies, Yeditepe University,Ataşehir,Istanbul, Turkey and The Institute for Graduate Studies in Sciences and Engineering, Yeditepe University, İstanbul Turkey. (E-mail: [email protected]) Abstract: The Sprott C and D systems are among the three variable simplest chaotic systems with resonant normal form characteristics and serve as possible candidates for demonstrating Hopf Bifurcation. Investigation of Sprott systems for deriving jerky Dynamics has also become of interest. The jerky dynamics has been analyzed with approximating discontinuities with a continuous function. In this work, we will use slightly generalized forms of these two Sprott systems, derive jerky systems compatible with them, analyze their transition to chaotic behavior and their attractors using ou...
In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modif... more In this article dynamical behavior of coupled Duffing oscillators is analyzed under a small modification. The oscillators have cubic damping instead of linear one. Although single duffing oscillator has complex dynamics, coupled duffing systems possess a much more complex structure. The dynamical behavior of the system is investigated both numerically and analytically. Numerical results indicate that the system has double scroll attractor with suitable parameter values. On the other hand, bifurcation diagrams illustrate rich behavior of the system, and it is seen that, system enters into chaos with different routes. Beside classical bifurcations, bubbling route to chaos is observed for suitable parameter settings. On the other hand, Multistability of the system is indicated with the coexisting attractors, such that under same parameter setting the system shows different periodic and chaotic attractors. Moreover, chaotic synchronization of coupled oscillators is illustrated in final ...
11th Chaotic Modeling and Simulation International Conference
Many models of physical systems involving electronic circuit elements [6], population dynamics [5... more Many models of physical systems involving electronic circuit elements [6], population dynamics [5] involve evolution equations with discontinuities. The key to understand such systems is to hope that the discontinuity does not adversely affect the integration process. There are also three variable chaotic dynamical system examples, such as the Sprott systems for deriving jerky dynamics that have also become of interest [10]. In order to calculate dynamical invariants in chaotic systems such as characteristic exponents and fractal dimensions we often need to find the Jacobian; this often requires attempting to differentiate discontinuous functions. Therefore finding a suitable continuous approximation to the discontinuities becomes important. In previous communications, two example systems had been used with two parametrizations for approximating discontinuous functions with continuous ones, one of which is the same as that used in the literature. In this work, we will use further examples to optimize the parameters of the continuous approximation to discontinuities using different examples in order to test the degree of applicability of this approach. Where possible, the invariants calculated by this method will be compared to the corresponding invariants calculated from its time series.
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Papers by Engin Kandiran