Dynamical order, disorder and propagating defects in homogeneous system of relaxation oscillators

TL;DR

This paper explores complex spatio-temporal patterns in coupled relaxation oscillators, revealing phenomena like anti-phase synchronization, oscillatory death, chimera states, and propagating defects, with implications for biological and chemical systems.

Contribution

It provides analytical insights into pattern formation and reports novel phenomena such as chimera states and propagating defects in a generic RD-inspired oscillator model.

Findings

Anti-phase synchronization explained analytically

Discovery of chimera states with coexisting dynamics

Propagating phase defects resembling cellular automata structures

Abstract

Reaction-diffusion (RD) mechanisms in chemical and biological systems can yield a variety of patterns that may be functionally important. We show that diffusive coupling through the inactivating component in a generic model of coupled relaxation oscillators give rise to a wide range of spatio-temporal phenomena. Apart from analytically explaining the genesis of anti-phase synchronization and spatially patterned oscillatory death regimes in the model system, we report the existence of a chimera state, characterized by spatial co-occurrence of patches with distinct dynamics. We also observe propagating phase defects in both one- and two-dimensional media resembling persistent structures in cellular automata, whose interactions may be used for computation in RD systems.