nonlocal coupling

Chimera Structures in Ensembles of Nonlocally Coupled Sprott Maps

Authors: Puzanov A. M., Anishchenko V. S., Strelkova G. I.

Background and Objectives: Recently, special attention in nonlinear dynamics and related research fields was targeted to the study of chimera states in networks of coupled oscillators. Chimeras were revealed in ensembles of nonlocally coupled identical systems which are described by both discrete- and continuous-time chaotic systems. In the paper we study numerically the dynamics of ring networks of nonlocally coupled chaotic discrete maps in order to find chimera states of different types, namely, phase and amplitude chimeras.

Spiral Wave Patterns in Two-Layer 2D Lattices of Nonlocally Coupled Discrete Oscillators. Synchronization of Spiral Wave Chimeras

Authors: Bukh A. V., Strelkova G. I., Anishchenko V. S.

The paper describes the spatio-temporal dynamics of a lattice that is given by a 2D N × N network of nonlocally coupled Nekorkin maps which model neuronal activity. The network behavior is studied for periodic and no-flux boundary conditions. It is shown that for certain values of the coupling parameters, rotating spiral waves and spiral wave chimeras can be observed in the considered lattice. We analyze and compare statistical and dynamical characteristics of the local oscillators from coherence and incoherence clusters of a spiral wave chimera.

Spatiotemporal Structures in an Ensemble of Nonlocally Coupled Nekorkin Maps

Authors: Bogomolov S. А., Rybalova E. V., Strelkova G. I., Anishchenko V. S.

Background and Objectives: Studying chimera states is a subject of special attention among specialists in nonlinear dynamics, and the issue on the mechanisms for implementing chimeras is today one of the topic directions. In the paper we consider the mechanism for realizing a chimera state regime which is based on the so-called “solitary states” (SSC) and is actively discussed by experts. The problem is solved by analyzing the dynamics of a one-dimensional ring of nonlocally coupled discrete-time systems.

Synchronization of Chimera States in Ensembles of Nonlocally Coupled Cubic Maps

Authors: Anishchenko V. S., Kholuianova I. А., Bogomolov S. А.

Background and Objectives: Effects of mutual and external synchronization of chimera states are studied in two coupled ensembles of discrete maps. Each of the ensembles is a onedimensional ring of nonlocally coupled cubic maps in the chaotic oscillation mode. In order to create differences in the dynamics of the ensembles when there is no coupling between them, a mismatch is introduced in the parameters of the individual oscillators of the first and second rings. Effects of external and mutual synchronization of chimera states are explored in detail.