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


Dynamics of the Rabinovich–Fabrikant system and its generalized model in the case of negative values of parameters that have the meaning of dissipation coefficients

Purpose of this work is a numerical study of the Rabinovich–Fabrikant system and its generalized model, which describe the occurrence of chaos during the parametric interaction of three modes in a nonequilibrium medium with cubic nonlinearity, in the case when the parameters that have the meaning of dissipation coefficients take negative values. These models demonstrate a rich dynamics that differs in many respects from what was observed for them, but in the case of positive values of the parameters. Methods.

On existence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with complex topology of attractor

Aim of this work is to study the possibility of existence of multistability near the boundary of generalized synchronization in systems with complex attractor topology. Unidirectionally coupled Lorentz systems have been chosen as an object of study, and a modified auxiliary system method has been used to detect the presence of the synchronous regime. Result of the work is a proof of the presence of multistability near the boundary of generalized synchronization in unidirectionally coupled systems with a complex topology of attractor.

Generalized Rabinovich–Fabrikant system: equations and its dynamics

The purpose of this work is to numerically study of the generalized Rabinovich–Fabrikant model. This model is obtained using the Lagrange formalism and describing the three-mode interaction in the presence of a general cubic nonlinearity. The model demonstrates very rich dynamics due to the presence of third-order nonlinearity in the equations. Methods. The study is based on the numerical solution of the obtained analytically differential equations, and their numerical bifurcation analysis using the MаtCont program. Results.

Approaches to study of multistability in spatio-temporal dynamics of two-age population

Purpose of the work is to study spatio-temporal dynamics of limited two-age structured populations that populate a 2D habitat and capable of long-range displacement of individuals. We proposed the model that is the network of nonlocally coupled nonlinear maps with nonlinear coupling function. Conditions for the emergence of different types of heterogeneous spatial distribution, combining coherent and incoherent regimes in different sites and solitary states are studied. Methods.

Multistability and memory effects in dynamical system with cosymmetric potential

The purpose of present study is the analysis of strong multistability in a dynamical system with cosymmetry. We study the dynamics and realization of steady-states in a mechanical system with two degrees of freedom. The minimum potential energy of the system is achieved on a curve in the form of an ellipse, which gives rise to a continuum family of equilibria and strong multistability. This problem belongs to the class of dynamical systems with cosymmetry. Methods.

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.

Dynamics of weakly dissipative self-oscillatory system at external pulse influence, which amplitude is depending polynomially on the dynamic variable

Topic and aim. In this work, we study the dynamics of the kicked van der Pol oscillator with the amplitude of kicks depending nonlinearly on the dynamic variable. We choose the expansions of the function cos x in a Taylor series near zero, as functions describing this dependence.

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.

Dynamic regimes and multistability in the system of non-symmetrically coupled two-dimensional maps with period-doubling and Neimark–Sacker bifurcations

The phenomenon of multistability in the system of coupled universal two-dimensional maps which shows period-doubling and Neimark–Sacker bifurcations is investigated. The decreasing of possible coexisting attractors number, the evolution of the attractor basins, the disappearance of hyperchaos and three-dimensional torus while putting coupling asymmetry are exposed.

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.