Amplitude mediated spiral chimera pattern in a nonlinear reaction-diffusion system

TL;DR

This paper investigates the emergence of amplitude mediated spiral chimera patterns in a reaction-diffusion prey-predator system, revealing transitions among various spatial patterns driven by diffusion parameters.

Contribution

It demonstrates the formation of spiral chimera states in a prey-predator model, a novel observation in reaction-diffusion systems with detailed transition analysis.

Findings

Identification of four distinct spatial patterns including spiral chimera.

Chimera states occur during transition from oscillatory to steady states.

Characterization of pattern strength and transition scenarios across diffusion parameters.

Abstract

Formation of diverse patterns in spatially extended reaction-diffusion systems is an important aspect of study which is pertinent to many chemical and biological processes. Of special interest is the peculiar phenomenon of chimera state having spatial coexistence of coherent and incoherent dynamics in a system of identically interacting individuals. In the present article, we report the emergence of various collective dynamical patterns while considering a system of prey-predator dynamics in presence of a two-dimensional diffusive environment. Particularly, we explore the observance of four distinct categories of spatial arrangements among the species, namely spiral wave, spiral chimera, completely synchronized oscillations, and oscillation death states in a broad region of the diffusion-driven parameter space. Emergence of amplitude mediated spiral chimera states displaying drifted amplitudes and phases in the incoherent subpopulation is detected for parameter values beyond both Turing and Hopf bifurcations. Transition scenarios among all these distinguishable patterns are numerically demonstrated for a wide range of the diffusion coefficients which reveal that the chimera states arise during the transition from oscillatory to steady state dynamics. Furthermore, we characterize the occurrence of each of the recognizable patterns by estimating the strength of incoherent subpopulations in the two-dimensional space.