G. V. Osipov

Learn More
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(More)
We extend the notion of phase locking to the case of chaotic oscillators. Different definitions of the phase are discussed, and the phase dynamics of a single self-sustained chaotic oscillator subjected to external force is investigated. We describe regimes where the amplitude of the oscillator remains chaotic and the phase is synchronized by the external(More)
We study phase synchronization in a chain of weakly coupled chaotic oscillators. In the synchronous state, the phases of oscillators are locked, while the amplitudes remain chaotic. We demonstrate that the coexistence of several clusters of mutually synchronized elements and global synchronization of all oscillators is possible. Two mechanisms of the(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(More)
Synchronization in large ensembles of coupled interacting units is a fundamental phenomenon relevant for the understanding of working mechanisms in neuronal networks, genetic networks, coupled electrical and laser networks, coupled mechanical systems, networks in social sciences, and others. It relates to mathematical and computational analysis of the(More)
Here we propose mechanisms for controlling the movement and suppression of spiral waves in discrete excitable media. We show that the controlled drift and subsequent annihilation of a spiral wave can be achieved through the combination of two factors: the introduction of small spatial inhomogeneities in the medium and the interaction of the wave with the(More)
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(More)
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(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(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(More)