Biomedical subjects

Grigory V Osipov

Publications and source records attributed to Grigory V Osipov.

8 recordsLinked to original sources

PubMed2005

Synchronized chaotic intermittent and spiking behavior in coupled map chains.

We study phase synchronization effects in a chain of nonidentical chaotic oscillators with a type-I intermittent behavior. Two types of parameter distribution, linear and random, are considered. The typical phenomena are the onset and existence of global (all-to-all) and cluster (partial) synchronization with increase of coupling. Increase of coupling strength can also lead to desynchronization phenomena, i.e., global or cluster synchronization is changed into a regime where synchronization is intermittent with incoherent states. Then a regime of a fully incoherent nonsynchronous state (spatiotemporal intermittency) appears. Synchronization-desynchronization transitions with increase of coupling are also demonstrated for a system resembling an intermittent one: a chain of coupled maps replicating the spiking behavior of neurobiological networks.

Journal Article↗

PubMed2004

Phase synchronization in ensembles of bursting oscillators.

We study the effects of mutual and external chaotic phase synchronization in ensembles of bursting oscillators. These oscillators (used for modeling neuronal dynamics) are essentially multiple time scale systems. We show that a transition to mutual phase synchronization takes place on the bursting time scale of globally coupled oscillators, while on the spiking time scale, they behave asynchronously. We also demonstrate the effect of the onset of external chaotic phase synchronization of the bursting behavior in the studied ensemble by a periodic driving applied to one arbitrarily taken neuron. We also propose an explanation of the mechanism behind this effect. We infer that the demonstrated phenomenon can be used efficiently for controlling bursting activity in neural ensembles.

Journal Article↗

PubMed2004

Phase synchronization of chaotic intermittent oscillations.

We study phase synchronization effects of chaotic oscillators with a type-I intermittency behavior. The external and mutual locking of the average length of the laminar stage for coupled discrete and continuous in time systems is shown and the mechanism of this synchronization is explained. We demonstrate that this phenomenon can be described by using results of the parametric resonance theory and that this correspondence enables one to predict and derive all zones of synchronization.

Journal Article↗

PubMed2003

Three types of transitions to phase synchronization in coupled chaotic oscillators.

We study the effect of noncoherence on the onset of phase synchronization of two coupled chaotic oscillators. Depending on the coherence properties of oscillations characterized by the phase diffusion, three types of transitions to phase synchronization are found. For phase-coherent attractors this transition occurs shortly after one of the zero Lyapunov exponents becomes negative. At rather strong phase diffusion, phase locking manifests a strong degree of generalized synchronization, and occurs only after one positive Lyapunov exponent becomes negative. For intermediate phase diffusion, phase synchronization sets in via an interior crises of the hyperchaotic set.

Journal Article↗

PubMed2003

Oscillatory and rotatory synchronization of chaotic autonomous phase systems.

The existence of rotatory, oscillatory, and oscillatory-rotatory synchronization of two coupled chaotic phase systems is demonstrated in the paper. We find four types of transition to phase synchronization depending on coherence properties of motions, characterized by phase variable diffusion. When diffusion is small the onset of phase synchronization is accompanied by a change in the Lyapunov spectrum; one of the zero Lyapunov exponents becomes negative shortly before this onset. If the diffusion of the phase variable is strong then phase synchronization and generalized synchronization, occur simultaneously, i.e., one of the positive Lyapunov exponents becomes negative, or generalized synchronization even sets in before phase synchronization. For intermediate diffusion the phase synchronization appears via interior crisis of the hyperchaotic set. Soft and hard transitions to phase synchronization are discussed.

Journal Article↗

PubMed2002

Locking-based frequency measurement and synchronization of chaotic oscillators with complex dynamics.

We propose a method for the determination of a characteristic oscillation frequency for a broad class of chaotic oscillators generating complex signals. It is based on the locking of standard periodic self-sustained oscillators by an irregular signal. The method is applied to experimental data from chaotic electrochemical oscillators, where other approaches of frequency determination (e.g., based on Hilbert transform) fail. Using the method we characterize the effects of phase synchronization for systems with ill-defined phase by external forcing and due to mutual coupling.

Journal Article↗

PubMed2002

Phase synchronization of chaotic rotators.

We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.

Journal Article↗

PubMed2001

Regular and chaotic phase synchronization of coupled circle maps.

We study the effects of regular and chaotic phase synchronization in ensembles of coupled nonidentical circle maps (CMs) and find phase-locking regions for both types of synchronization. We show that synchronization of chaotic CMs is crucially influenced by the three quantities: (i) rotation number difference, (ii) variance of the phase evolution, and (iii)relative duration of intervals of phase increase respect decrease. In the case of regular CMs, only variance and rotation number difference are important. It is demonstrated that with increase of noncoherence of phase evolutionsin the regular and chaotic regime, the regions of the main (1:1) synchronization are usually decreased. We present a chaotic synchronization in the systems of coupled nonidentical circle maps where phase entrainment occurs and it is not accompanied by bifurcations of the chaotic set. For ensembles (chains) of coupled CMs with linear and random distributions of the individual frequencies soft and hard transitions to global synchronization are found.

Journal Article↗