Transition from chimera/solitary states to traveling waves

TL;DR

This study explores the complex spatiotemporal behaviors in a ring network of discretized van der Pol oscillators, revealing new transient chimera and solitary states and analyzing their transition to traveling waves.

Contribution

It introduces a detailed numerical analysis of a discretized van der Pol oscillator network, discovering novel transient states and their transition dynamics.

Findings

Discovery of coexistence of multichimera and traveling wave states.

Identification of solitary states as transient phenomena.

Analysis of how system parameters influence transient durations.

Abstract

We study numerically the spatiotemporal dynamics in a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. It is shown that the discretized oscillator exhibits a richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Regimes such as the coexistence of multichimera state/traveling wave and solitary state are revealed for the first time and are studied in detail. It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient towards the purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, the observation time, initial conditions, and the influence of external noise.