ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

spatial structures

Wave processes in a ring of memristively coupled self-excited oscillators

The purpose of this work is to reveal intrinsic peculiarities of the dynamics and spatial structure formation in an ensemble of the coupled van der Pol self-oscillators in a case of memristive coupling. Two models of memristive coupling are considered: an idealised memristive model and a real one exhibiting the effect of «forgetting» of an initial state after a long time. Methods. Numerical simulation of the equations describing the system under study by means of the fourthorder Runge–Kutta method is carried out.

Strange waves in the ensemble of van der Pol oscillators

The purpose of this paper is to study the processes of spatial disorder and the development of phase multistability in a discrete medium of anharmonic oscillators. Methods. An ensemble of diffusively coupled van der Pol oscillators is used as a model of discrete anharmonic medium. The model is investigated by numerical simulation; its phase dynamics is studied. The formed spatial structures are visualized by means of phase difference distribution. Results.

External synchronization of traveling waves in an active medium in self-sustained and excitable regime

The model of a one-dimensional active medium, which cell represents FitzHugh–Nagumo oscillator, is studied with periodical boundary conditions. Such medium can be either self-oscillatory or excitable one in dependence of the parameters values. Periodical boundary conditions provide the existence of traveling wave regimes both in excitable anself-oscillatory case without any deterministic or stochastic impacts.

Period doubling bifurcations and noise excitation effects in a multistable self-sustained oscillatory medium

The model of a self-oscillatory medium composed from the elements with complex self-oscillatory behavior is studied. Under periodic boundary conditions the stable selfoscillatory regimes in the form of traveling waves with different phase shifts are coexisted in medium. The study of mechanisms of the oscillations period doubling in time is performed for different coexisted modes. For all observed spatially-non-uniform regimes (traveling waves) the period doubling occurs through the appearance of time-quasiperiodic oscillations and their further evolution.

Mixing and diffusion effect on spatial-temporal dynamics in stochastic Lotka–Volterra system with discrete phase space

The influence of two types of diffusion on dynamics of stochastic lattice Lotka– Volterra model is considered in this work. The simulations were carried out by means of Kinetic Monte-Carlo algorithm. It is shown that the local diffusion considerably changes the dynamics of the model and accelerates the interaction processes on the lattice, while the mixing results in appearance of global periodic oscillations. The global oscillations appear due to phenomenon of phase synchronization.