multistability

Aim. The aim of the investigation is to study the regularities of phase multistability in an ensemble of oscillatory systems with non-local couplings in dependance of strength and radius of the couplings, as well as to describe them from the point of view of the spatial spectrum.

The paper is devoted to the study of noise-induced intermittent behavior in multistable systems. Such task is an important enough because despite of a great interest of investigators to the study of multistability and intermittency, the problem connected with the detailed understanding of the processes taking place in the multistable dynamical systems in the presence of noise and theoretical description of arising at that intermittent behavior is still remain unsolved.

The work is devoted to study of multistability of traveling waves in a ring of harmonic oscillators with a linear non-local couplings. It analyses the influence of the strength and radius of the couplings on stability of spatially periodic regimes with different values of their wavelengths. The system under study is an array of identical van der Pol generators in the approximation of quasi-harmonic oscillations.

The work is devoted to investigation of multistability of running waves in a ring of periodic oscillators with diffusive non-local couplings. It analyzes the influence of long-range couplings and their change with distance on the stability of spatially-periodic regimes with different wave numbers.

Multistable regimes in asymmetrically coupled logistic maps are investigated. The evolution of the multistability regions in the parameter plane and the basins of coexisting attractors are revealed.

In this paper we study the bifurcational mechanisms of synchronization and multistability formation in a system of two interacting van der Pol oscillators, one of which is under external harmonic forcing. We draw a two­parametric bifurcation diagram for phasereduced system and study its evolution in transition from symmetrical to asymmetrical repulsive interaction. Relying on the results of bifurcation analysis of non­reduced system we conclude that the synchronization scenarios found in the phase­reduced system correspond to the ones in the non­reduced system.

Synchronization is studied in ensembles of locally dissipative coupled and conservative coupled weak-nonlinear van der Pol oscillators. In the chain of N elements not less than 2N¡1 different regimes of global synchronization are stable at the same values of parameters. Cluster synchronization is considered as well. Existing of multiple fronts of synchronization switching is shown. These fronts go one through another without of changing or reflections from free boundaries.

We study synchronization in one- and two-dimentional ensembles of nonidentical Bonhoeffer–van der Pol oscillators. Small chains (number of elements N 6 4) are proved to have not less than 2N¡1 coexisting stable different synchronous regimes. The chain of N elements is supposed to have not less than 2N¡1 synchronous regimes at the same values of parameters. Formation of synchronization clusters at weak coupling is shown. Regimes, provided by existing of waves, setting rhythm for all elements in ensemble, are investigated.

We study synchronization of two coupled nonidentical Bonhoeffer–van der Pol oscillators. Coexistence of two different synchronous regimes is proved. Mechanisms of synchronous regimes origination and destruction are investigated. Fluctuations influence on syncronous regimes is considered. It is found that noise can cause: i) synchronization destruction and beating originations; ii) fluctuations-caused bistability destruction; iii) fluc-tuations-caused intermittency of synchronous regimes without synchronization destruction.

Regularities of multistability developments are considered in an array of identical self­sustained oscillators with transition to chaos through period­doubling bifurcations. The used model is chain of diffusivelly coupled Rossler oscillators. The number of coexisting regimes are determined through the cascade of the bifurcations. It is shown that regularities of incresing of attractors are defined be transformation of the phase spectrum duing transition to chaos.