Dynamics of a 2D lattice of van der Pol oscillators with nonlinear repulsive coupling

TL;DR

This paper investigates complex spatiotemporal patterns, including chimera states, in a 2D lattice of van der Pol oscillators with nonlinear repulsive coupling, revealing new solitary state phenomena and their evolution.

Contribution

It introduces the first observation of solitary state chimeras in continuous-time oscillator systems and details their formation and transition mechanisms.

Findings

Spiral wave chimeras form at high coupling strength with short range.

Target wave chimeras involve solitary states that spread within coherence clusters.

Solitary states evolve with increasing coupling range and strength, leading to new spatiotemporal regimes.

Abstract

We describe spatiotemporal patterns in a network of identical van der Pol oscillators coupled in a two-dimensional geometry. In this study, we show that the system under study demonstrates a plethora of different spatiotemporal structures including chimera states when the coupling parameters are varied. Spiral wave chimeras are formed in the network when the coupling strength is rather large and the coupling range is short enough. Another type of chimeras is a target wave chimera. It is shown that solitary states play a crucial role in forming an incoherence cluster of this chimera state. They can also spread within the coherence cluster. Furthermore, when the coupling range increases, the target wave chimera evolves to the regime of solitary states which are randomly distributed in space. Growing the coupling strength leads to the attraction of solitary states to a certain spatial region, while the synchronous regime is set in the other part of the system. This spatiotemporal pattern represents a solitary state chimera, which is firstly found in the system of continuous-time oscillators. We offer the explanation of these phenomena and describe the evolution of the regimes in detail.