Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
In one-dimensional piecewise smooth maps with multiple borders, chaotic attractors may undergo bo... more In one-dimensional piecewise smooth maps with multiple borders, chaotic attractors may undergo border collision bifurcations, leading to a sudden change in their structure. We describe two types of such border collision bifurcations and explain the mechanisms causing the changes in the geometrical structure of the attractors, in particular, in the number of their bands (connected components).
Physical experiments have long revealed that impact oscillators commonly exhibit large-amplitude ... more Physical experiments have long revealed that impact oscillators commonly exhibit large-amplitude chaos over a narrow band of parameter values close to grazing bifurcations. This phenomenon is not explained by the squareroot singularity of the Nordmark map, which captures the local dynamics to leading order, because this map does not exhibit such dynamics. In this paper, we compare a Poincaré map for a prototypical impact oscillator model with the corresponding Nordmark map. Though the maps agree to leading order, the Poincaré map exhibits a large-amplitude chaotic attractor while the Nordmark map does not because part of the attractor resides in a region of phase space where the two maps differ significantly.
Objective: to examine the state of the immunity to measles in different age groups.Materials and ... more Objective: to examine the state of the immunity to measles in different age groups.Materials and methods: In 2018, 4444 people were examined at the Diagnostic Center (virological). Among them, 3783 people were examined using the passive haemagglutination test for measles (manufactured by Pasteur Research Institute of Epidemiology and Microbiology, Russia). In the remaining 661 cases, the IgG to measles were detected using the enzyme-linked immunosorbent assay (ELISA) by VektoMeaseles IgG test (manufactured by Vector-Best, Russia). The correlation between the measles IgG level (ELISA) and the age was examined in 518 patients. Results: In this study, the immunity to measles was shown to be insufficient in all groups of observed people. Even among medical staff, nearly 10% had no protective level of measles antibodies. We have shown that the correlation between the measles IgG level and the age is statistically significant, so that the number of seronegative persons in different age gr...
In this work we investigated to which extent the evaluation results of the degree of hepatic fibr... more In this work we investigated to which extent the evaluation results of the degree of hepatic fibrosis obtained by realtime elastography (RTE) method are compatible with the results of the transient elastography (TE) and with the APRI indexes. We also analyzed the factors which can influence the reliability of the fibrosis degree evaluation obtained by different methods.Materials and methods. The study included 99 patients (60 women and 39 men) with HCV, examined in the polyclinic department of the Saint-Petersburg Botkin clinical infectious hospital in 2017. In 83 patients, the fibrosis degree in the liver tissue has been evaluated by the RTE method using HI VISION Preirus (Hitachi, Japan) with a linear sensor. In 67 patients, the evaluation has been performed by the TE method using Fibroscan (Echosens, France). Both methods have been applied to 51 patients.Conclusions. The aplication results of the RTE and TE methods do not differ significantly for patients with a severe fibrosis. ...
The paper describes how several coexisting stable closed invariant curves embedded into each othe... more The paper describes how several coexisting stable closed invariant curves embedded into each other can arise in a two-dimensional piecewise-linear normal form map. Phenomena of this type have been recently reported for a piecewise smooth map, modeling the behavior of a power electronic DC–DC converter. In the present work, we demonstrate that this type of multistability exists in a more general class of models and show how it may result from the well-known period adding bifurcation structure due to its deformation so that the phase-locking regions start to overlap. We explain how this overlapping structure is related to the appearance of coexisting stable closed invariant curves nested into each other. By means of detailed, numerically calculated phase portraits we hereafter present an example of this type of multistability. We also demonstrate that the basins of attraction of the nested stable invariant curves may be separated from each other not only by repelling closed invariant ...
Dynamical behaviors arising in a previously developed pulse-modulated mathematical model of non-b... more Dynamical behaviors arising in a previously developed pulse-modulated mathematical model of non-basal testosterone regulation in the human male due to continuous exogenous signals are studied. In the context of endocrine regulation, exogenous signals represent, e.g., the influx of a hormone replacement therapy drug, the influence of the circadian rhythm, and interactions with other endocrine loops. This extends the scope of the autonomous pulse-modulated models of endocrine regulation to a broader class of problems, such as therapy optimization, but also puts it in the context of biological rhythms studied in chronobiology. The model dynamics are hybrid since the hor
A dangerous border collision bifurcation has been defined as the dynamical instability that occur... more A dangerous border collision bifurcation has been defined as the dynamical instability that occurs when the basins of attraction of stable fixed points shrink to a set of zero measure as the parameter approaches the bifurcation value from either side. This results in almost all trajectories diverging off to infinity at the bifurcation point, despite the eigenvalues of the fixed points before and after the bifurcation being within the unit circle. In this paper, we show that similar bifurcation phenomena also occur when the stable orbit in question is of a higher periodicity or is chaotic. Accordingly, we propose a generalized definition of dangerous bifurcation suitable for any kind of attracting sets. We report two types of dangerous border collision bifurcations and show that, in addition to the originally reported mechanism typically involving singleton saddle cycles, there exists one more situation where the basin boundary is formed by a repelling closed invariant curve.
Piecewise-smooth dynamical systems are characterized by the fact that their state space is divide... more Piecewise-smooth dynamical systems are characterized by the fact that their state space is divided into partitions by borders also denoted as switching manifolds. Within each partition, the system is smooth (that is C k up to some k) but the rules which govern the dynamic behavior (that ...
Power factor correction converters are used in many applications as AC-DC power supplies aiming a... more Power factor correction converters are used in many applications as AC-DC power supplies aiming at maintaining a near unity power factor. Systems of this type are known to exhibit nonlinear phenomena such as sub-harmonic oscillations and chaotic regimes that cannot be described by traditional averaged models. In this paper, we derive a time varying discretetime map modeling the behavior of a power factor correction AC-DC boost converter. This map is derived in closed-form and is able to faithfully reproduce the system behavior under realistic conditions. In the chaotic regime the map exhibits a sequence of bifurcation similar to a bandcount doubling cascade on the low frequency. However, the observed scenario appears in some sense incomplete, with some gaps in the bifurcation diagram, whose appearance to our knowledge has never been reported before. We show that these gaps are caused by high frequency oscillations.
In this paper we present an automatic design of neural controllers for robots using a method call... more In this paper we present an automatic design of neural controllers for robots using a method called Evolutionary Acquisition of Neural Topologies (EANT). The method evolves both the structure and weights of neural networks. It starts with networks of minimal structures determined by the domain expert and increases their complexity along the evolution path. It introduces an efficient and compact genetic encoding of neural networks onto a linear genome that enables one to evaluate the network without decoding it. The method uses a meta-level evolutionary process where new structures are explored at larger timescale and existing structures are exploited at smaller timescale. We demonstrate the method by designing a neural controller for a real robot which should be able to move continously in a given environment cluttered with obstacles. We first give an introduction to the evolutionary method and then describe the experiments and results obtained.
This article describes a novel bifurcation phenomenon occurring in the 2D parameter space of piec... more This article describes a novel bifurcation phenomenon occurring in the 2D parameter space of piecewise-linear maps. In the region of chaotic behavior we detect an infinite number of interior crises bounding the regions of multi-band attractors. This phenomenon, denoted as bandcount adding scenario, leads to a self-similar structure of the chaotic region in the parameter space.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
In one-dimensional piecewise smooth maps with multiple borders, chaotic attractors may undergo bo... more In one-dimensional piecewise smooth maps with multiple borders, chaotic attractors may undergo border collision bifurcations, leading to a sudden change in their structure. We describe two types of such border collision bifurcations and explain the mechanisms causing the changes in the geometrical structure of the attractors, in particular, in the number of their bands (connected components).
Physical experiments have long revealed that impact oscillators commonly exhibit large-amplitude ... more Physical experiments have long revealed that impact oscillators commonly exhibit large-amplitude chaos over a narrow band of parameter values close to grazing bifurcations. This phenomenon is not explained by the squareroot singularity of the Nordmark map, which captures the local dynamics to leading order, because this map does not exhibit such dynamics. In this paper, we compare a Poincaré map for a prototypical impact oscillator model with the corresponding Nordmark map. Though the maps agree to leading order, the Poincaré map exhibits a large-amplitude chaotic attractor while the Nordmark map does not because part of the attractor resides in a region of phase space where the two maps differ significantly.
Objective: to examine the state of the immunity to measles in different age groups.Materials and ... more Objective: to examine the state of the immunity to measles in different age groups.Materials and methods: In 2018, 4444 people were examined at the Diagnostic Center (virological). Among them, 3783 people were examined using the passive haemagglutination test for measles (manufactured by Pasteur Research Institute of Epidemiology and Microbiology, Russia). In the remaining 661 cases, the IgG to measles were detected using the enzyme-linked immunosorbent assay (ELISA) by VektoMeaseles IgG test (manufactured by Vector-Best, Russia). The correlation between the measles IgG level (ELISA) and the age was examined in 518 patients. Results: In this study, the immunity to measles was shown to be insufficient in all groups of observed people. Even among medical staff, nearly 10% had no protective level of measles antibodies. We have shown that the correlation between the measles IgG level and the age is statistically significant, so that the number of seronegative persons in different age gr...
In this work we investigated to which extent the evaluation results of the degree of hepatic fibr... more In this work we investigated to which extent the evaluation results of the degree of hepatic fibrosis obtained by realtime elastography (RTE) method are compatible with the results of the transient elastography (TE) and with the APRI indexes. We also analyzed the factors which can influence the reliability of the fibrosis degree evaluation obtained by different methods.Materials and methods. The study included 99 patients (60 women and 39 men) with HCV, examined in the polyclinic department of the Saint-Petersburg Botkin clinical infectious hospital in 2017. In 83 patients, the fibrosis degree in the liver tissue has been evaluated by the RTE method using HI VISION Preirus (Hitachi, Japan) with a linear sensor. In 67 patients, the evaluation has been performed by the TE method using Fibroscan (Echosens, France). Both methods have been applied to 51 patients.Conclusions. The aplication results of the RTE and TE methods do not differ significantly for patients with a severe fibrosis. ...
The paper describes how several coexisting stable closed invariant curves embedded into each othe... more The paper describes how several coexisting stable closed invariant curves embedded into each other can arise in a two-dimensional piecewise-linear normal form map. Phenomena of this type have been recently reported for a piecewise smooth map, modeling the behavior of a power electronic DC–DC converter. In the present work, we demonstrate that this type of multistability exists in a more general class of models and show how it may result from the well-known period adding bifurcation structure due to its deformation so that the phase-locking regions start to overlap. We explain how this overlapping structure is related to the appearance of coexisting stable closed invariant curves nested into each other. By means of detailed, numerically calculated phase portraits we hereafter present an example of this type of multistability. We also demonstrate that the basins of attraction of the nested stable invariant curves may be separated from each other not only by repelling closed invariant ...
Dynamical behaviors arising in a previously developed pulse-modulated mathematical model of non-b... more Dynamical behaviors arising in a previously developed pulse-modulated mathematical model of non-basal testosterone regulation in the human male due to continuous exogenous signals are studied. In the context of endocrine regulation, exogenous signals represent, e.g., the influx of a hormone replacement therapy drug, the influence of the circadian rhythm, and interactions with other endocrine loops. This extends the scope of the autonomous pulse-modulated models of endocrine regulation to a broader class of problems, such as therapy optimization, but also puts it in the context of biological rhythms studied in chronobiology. The model dynamics are hybrid since the hor
A dangerous border collision bifurcation has been defined as the dynamical instability that occur... more A dangerous border collision bifurcation has been defined as the dynamical instability that occurs when the basins of attraction of stable fixed points shrink to a set of zero measure as the parameter approaches the bifurcation value from either side. This results in almost all trajectories diverging off to infinity at the bifurcation point, despite the eigenvalues of the fixed points before and after the bifurcation being within the unit circle. In this paper, we show that similar bifurcation phenomena also occur when the stable orbit in question is of a higher periodicity or is chaotic. Accordingly, we propose a generalized definition of dangerous bifurcation suitable for any kind of attracting sets. We report two types of dangerous border collision bifurcations and show that, in addition to the originally reported mechanism typically involving singleton saddle cycles, there exists one more situation where the basin boundary is formed by a repelling closed invariant curve.
Piecewise-smooth dynamical systems are characterized by the fact that their state space is divide... more Piecewise-smooth dynamical systems are characterized by the fact that their state space is divided into partitions by borders also denoted as switching manifolds. Within each partition, the system is smooth (that is C k up to some k) but the rules which govern the dynamic behavior (that ...
Power factor correction converters are used in many applications as AC-DC power supplies aiming a... more Power factor correction converters are used in many applications as AC-DC power supplies aiming at maintaining a near unity power factor. Systems of this type are known to exhibit nonlinear phenomena such as sub-harmonic oscillations and chaotic regimes that cannot be described by traditional averaged models. In this paper, we derive a time varying discretetime map modeling the behavior of a power factor correction AC-DC boost converter. This map is derived in closed-form and is able to faithfully reproduce the system behavior under realistic conditions. In the chaotic regime the map exhibits a sequence of bifurcation similar to a bandcount doubling cascade on the low frequency. However, the observed scenario appears in some sense incomplete, with some gaps in the bifurcation diagram, whose appearance to our knowledge has never been reported before. We show that these gaps are caused by high frequency oscillations.
In this paper we present an automatic design of neural controllers for robots using a method call... more In this paper we present an automatic design of neural controllers for robots using a method called Evolutionary Acquisition of Neural Topologies (EANT). The method evolves both the structure and weights of neural networks. It starts with networks of minimal structures determined by the domain expert and increases their complexity along the evolution path. It introduces an efficient and compact genetic encoding of neural networks onto a linear genome that enables one to evaluate the network without decoding it. The method uses a meta-level evolutionary process where new structures are explored at larger timescale and existing structures are exploited at smaller timescale. We demonstrate the method by designing a neural controller for a real robot which should be able to move continously in a given environment cluttered with obstacles. We first give an introduction to the evolutionary method and then describe the experiments and results obtained.
This article describes a novel bifurcation phenomenon occurring in the 2D parameter space of piec... more This article describes a novel bifurcation phenomenon occurring in the 2D parameter space of piecewise-linear maps. In the region of chaotic behavior we detect an infinite number of interior crises bounding the regions of multi-band attractors. This phenomenon, denoted as bandcount adding scenario, leads to a self-similar structure of the chaotic region in the parameter space.
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Papers by Viktor Avrutin