G. Osipov - Academia.edu (original) (raw)

Papers by G. Osipov

Physica Scripta, 1998

В работе исследовалась динамика двух упруго связанных между собой маятников одинаковой массы, нах... more В работе исследовалась динамика двух упруго связанных между собой маятников одинаковой массы, находящихся под действием разных постоянно действующих внешних вращательных моментов. Исследование мотивировано многочисленными физическими и биологическими приложениями рассматриваемой модели. Такие системы входят в число базовых физических моделей и представляют широкий научный интерес. На сегодняшний день существует немало работ, изучающих маятниковые ансамбли более высокого порядка. Представляется важным подробно и полно изучить динамику системы двух маятников, нелинейно связанных друг с другом, как базу для понимания поведения более сложных ансамблей фазовых осцилляторов. При изучении динамики двух нелинейно связанных маятников наибольший интерес представляет рассмотрение режима синхронизации, являющегося одним из основных режимов, наблюдаемых при взаимодействии нескольких осцилляторов в природе. Также в работе описываются и другие режимы, характеризующие динамику системы. Цель исследования состоит в изучении динамики системы в зависимости от параметров. Рассмотрены периодический и квазипериодический режимы колебаний, синхронизация и режим отсутствия колебаний. В работе получены оригинальные результаты, касающиеся аналитической оценки границы области синхронизации в плоскости {d, α}, где d-сила связи между осцилляторами, а α-параметр синхронизации. Для получения вышеуказанной оценки были проведены элементы качественного анализа систем нелинейно связанных уравнений Адлера. Аналитическая оценка была подтверждена результатами прямого численного моделирования системы. В работе использовался метод Рунге-Кутты четвёртого порядка с контролем локальной погрешности. Были построены бифуркационные диаграммы в плоскости {γ1, γ2} для различных значений параметра связи. Исследовано влияние параметров системы на существующие в ней режимы.

Frontiers in Neuroscience, 2016

Recent research has revealed a rich and complicated network topology in various model systems as ... more Recent research has revealed a rich and complicated network topology in various model systems as well as in several elds of applications. It will be discussed whether this approach can lead to useful new insights into rather large complex systems or whether it is fashionable only to interpret various phenomena from this viewpoint and publish papers on that. Among such studies it has become very popular to look for a scale- free behaviour by showing log-log plots. This reminds the hunting for low dimensional chaos in the 80ies of the last millennium. A challenging task is to understand the implications of such network structures on the functional organization of the brain activities. This is studied here basing on dynamical complex networks. We investigate synchronization dynamics on the cortico-cortical network of the cat by modelling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We nd that the network displays clus- tered synchronizat...

2000 2nd International Conference. Control of Oscillations and Chaos. Proceedings (Cat. No.00TH8521), 2000

ABSTRACT Recent findings indicate that fibrillating cardiac tissue arises from spiral wave chaos.... more ABSTRACT Recent findings indicate that fibrillating cardiac tissue arises from spiral wave chaos. Here we show that spiral wave chaos can be suppressed in a cardiac model by pacing the system with low-amplitude, high-frequency current pulses. This overdrive pacing technique is analyzed using a one-dimensional chain and a two-dimensional lattice of coupled, excitable elements with the kinetics described by the Luo-Rudy action potential model (1991). When two-dimensional media were excited with frequencies from 1:1 synchronization region, we found that spiral wave chaos could be suppressed in a limited number of cases. However, when used in conjunction with calcium channel blockers, high-frequency pacing suppressed spiral wave chaos in all episodes. These findings suggest that low-amplitude overdrive pacing in combination with class IV antiarrhythmic drugs, inhibitors of calcium channels, may be useful for eliminating fibrillation in cardiac tissue

Procedia Computer Science, 2013

This paper presents the results of the development of a biomedical software system at the Nizhni ... more This paper presents the results of the development of a biomedical software system at the Nizhni Novgorod State University High Performance Computing Competence Center. We consider four main fields: plasma simulation, heart activity simulation, brain sensing simulation, molecular dynamics simulation. The software system is aimed at large-scale simulation on cluster systems with high efficiency and scalability. We demonstrate current results of the numerical simulation, analyze performance and propose the ways to improve efficiency.

Physical Review Letters, 1997

The chaotically driven circle map is considered as the simplest model of phase synchronization of... more The chaotically driven circle map is considered as the simplest model of phase synchronization of a chaotic continuous-time oscillator by external periodic force. The phase dynamics is analyzed via phase-locking regions of the periodic cycles embedded in the strange attractor. It is shown that full synchronization, where all the periodic cycles are phase locked, disappears via the attractor-repeller collision. Beyond the transition an intermittent regime with exponentially rare phase slips, resulting from the trajectory's hits on an eyelet, is observed.

Physical Review E, 2013

In this work, we study the onset of sequential activity in ensembles of neuronlike oscillators wi... more In this work, we study the onset of sequential activity in ensembles of neuronlike oscillators with inhibitorylike coupling between them. The winnerless competition (WLC) principle is a dynamical concept underlying sequential activity generation. According to the WLC principle, stable heteroclinic sequences in the phase space of a network model represent sequential metastable dynamics. We show that stable heteroclinic sequences and stable heteroclinic channels, connecting saddle limit cycles, can appear in oscillatory models of neural activity. We find the key bifurcations which lead to the occurrence of sequential activity as well as heteroclinic sequences and channels.

EPL (Europhysics Letters), 2009

Page 1. Synchronization in growing heterogeneous media This article has been downloaded from IOPs... more Page 1. Synchronization in growing heterogeneous media This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2009 EPL 86 18001 (http://iopscience.iop.org/0295-5075/86/1/18001) ...

Chaos, Solitons & Fractals, 1998

The method of feedback impulsive suppression of chaos is introduced. Our approach is based on the... more The method of feedback impulsive suppression of chaos is introduced. Our approach is based on the similarity of return maps of some time continuous systems with one-dimensional cubic maps. The method is illustrated for the Duffing oscillator with positive linear stiffness by making use of its symmetry properties.

ABSTRACT We report here an interesting multiscroll dynamics in two undirectionally coupled Lorenz... more ABSTRACT We report here an interesting multiscroll dynamics in two undirectionally coupled Lorenz systems. The driver Lorenz system parametersa are set for the usual butterfly type attractor (2-scroll) while the response system is in resting state when uncoupled. We observed multiscroll attractors (3-, 4-, 5-, 6-scroll) at the response system in the weaker coupling regime. The multiscroll is seen as one after another additional scroll emerges in phase space of the response system with gradual decrease in coupling strength. The 3D attractors and their corresponding 2D phase portraits are shown in Fig.1. It appears as if a hidden multiscroll structure unfolds in the response oscillator, which is otherwise dormant in uncoupled state, when a butterfly type Lorenz attractor is forced into it and the forcing strength is weakened. The important practical applications of multiscroll are known as b roadband signal generator and true pseudorandom number generator for communication engineering.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 1997

We consider phase synchronization of chaotic continuous-time oscillator by periodic external forc... more We consider phase synchronization of chaotic continuous-time oscillator by periodic external force. Phase-locking regions are defined for unstable periodic cycles embedded in chaos, and synchronization is described in terms of these regions. A special flow construction is used to derive a simple discrete-time model of the phenomenon. It allows to describe quantitatively the intermittency at the transition to phase synchronization.

Physical Review E, 2009

In this paper we focus on the influence of passive elements on the collective dynamics of oscilla... more In this paper we focus on the influence of passive elements on the collective dynamics of oscillatory ensembles. Two major effects considered are ͑i͒ the influence of passive elements on the synchronization properties of ensembles of coupled nonidentical oscillators and ͑ii͒ the influence of passive elements on the wave dynamics of such systems. For the first effect, it is demonstrated that the introduction of passive elements may lead to both an increase or decrease in the global synchronization threshold. For the second effect, it is also demonstrated that the steady state of the passive element is a key parameter which defines how this passive element affects the wave dynamics of the oscillatory ensemble. It was shown that for different values of this parameter, one can observe increase or decrease in wave propagation velocity and increase or decrease in synchronization frequency in oscillatory ensembles with the growth of influence of passive elements. The results are obtained for the models of cardiac cells dynamics as well as for the Bonhoeffer-Van der Pol model and are compared with data of real biological experiments.

The European Physical Journal Special Topics, 2016

The motif of three inhibitory coupled Rulkov elements is studied. Possible dynamical regimes, inc... more The motif of three inhibitory coupled Rulkov elements is studied. Possible dynamical regimes, including different types of sequential activity, winner-take-all activity and chaotic activity, are in the focus of this paper. In particular, a new transition scenario from sequential activity to winner-take-all activity through chaos is uncovered. This study can be used in high performance computation of large neuron-like ensembles for the modeling of neuron-like activity.

Chaos: An Interdisciplinary Journal of Nonlinear Science, 2009

There is a growing body of evidence that slow brain rhythms are generated by simple inhibitory ne... more There is a growing body of evidence that slow brain rhythms are generated by simple inhibitory neural networks. Sequential switching of tonic spiking activity is a widespread phenomenon underlying such rhythms. A realistic generative model explaining such reproducible switching is a dynamical system that employs a closed stable heteroclinic channel (SHC) in its phase space. Despite strong evidence on the existence of SHC, the conditions on its emergence in a spiking network are unclear. In this paper, we analyze a minimal, reciprocally connected circuit of three spiking units and explore all possible dynamical regimes and transitions between them. We show that the SHC arises due to a Neimark-Sacker bifurcation of an unstable cycle.

Journal of electrocardiology, Dec 31, 2011

Sinoatrial node is responsible for the origin of the wave of excitation, which spreads throughout... more Sinoatrial node is responsible for the origin of the wave of excitation, which spreads throughout the heart and orchestrates cardiac contraction via calcium-mediated excitation-contraction coupling. P wave represents the spread of excitation in the atria. It is well known that the autonomic nervous system controls the heart rate by dynamically altering both cellular ionic fluxes and the anatomical location of the leading pacemaker. In this study, we used isolated rabbit right atria and mathematical model of the pacemaker region of the ...