Bistable labyrinth-like structures and chimera states in a 2D lattice of van der Pol oscillators

The present work is devoted to the numerical analysis of the dynamics of a 2D lattice of coupled van der Pol oscillators in the regime of relaxation oscillations. It is shown that the influence of coupling leads to the shift of effective values of the control parameters of individual oscillators. The strong coupling can even cause the transition to bistable dynamics which is never observed in a single van der Pol oscillator. The numerically constructed phase-parametric diagram that takes into account the shifts of parameters shows that the bistability arises through the pitchfork bifurcation when varying the coupling strength. The lattice dynamics is analyzed when the control and coupling parameters are varied within a wide range, and the regime diagrams are constructed in the planes of system parameters. A new type of spatiotemporal pattern, a so-called labyrinth-like structure, is found and described in detail. We also reveal for the first time and study a spiral wave chimera with a new kind of the incoherence core in the form of labyrinth-like structure. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study focuses on the dynamics of a 2D lattice of coupled van der Pol oscillators in the regime of relaxation oscillations, showing that coupling can lead to shifts in control parameters and even bistable dynamics. A numerically constructed phase-parametric diagram reveals the emergence of bistability through pitchfork bifurcation. Additionally, a new spatiotemporal pattern, called a labyrinth-like structure, is found and studied in detail.