Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

TL;DR

This paper investigates how solitary states influence the formation of complex spatiotemporal patterns in a 2D lattice of van der Pol oscillators, revealing new solitary and chimera states.

Contribution

It introduces the first observation of solitary state and solitary state chimera regimes in a 2D lattice of coupled van der Pol oscillators.

Findings

Incoherent and chimera-like regimes occur at low coupling strength.

Synchronization emerges with increased coupling parameters.

Novel solitary and solitary chimera states are identified in the lattice.

Abstract

The behavior of the ensemble of coupled van der Pol oscillators is abundant when coupling parameters are changed. Incoherent and chimera-like regimes are observed at small values of the coupling strength parameter. Synchronization takes place with an increase in the coupling strength and coupling range parameters. Various chimera and solitary states are realised when the coupling strength parameter is sufficiently large. The single van der Pol oscillator is taken in the regime of relaxation oscillations. Therefore, the lattice may realise spiral wave and spiral wave chimera regimes. Besides, target wave and solitary state regimes are observed in the ensemble. Finally, the solitary state and solitary state chimera regimes are firstly shown for the lattice of coupled van der Pol oscillators.