Turing instability in oscillator chains with non-local coupling

TL;DR

This paper analyzes the conditions under which Turing instability occurs in a one-dimensional chain of nonlinear oscillators with non-local power-law coupling, bridging local and global interaction regimes.

Contribution

It provides an analytical and numerical study of Turing instability in oscillator chains with non-local coupling, introducing a range parameter to unify local and global coupling scenarios.

Findings

Identifies conditions for Turing instability in non-local oscillator chains.

Shows how the range parameter influences pattern formation.

Applies analysis to a nonlinear auto-catalytic reaction-diffusion model.

Abstract

We investigate analytically and numerically the conditions for the Turing instability to occur in a one-dimensional chain of nonlinear oscillators coupled non-locally in such a way that the coupling strength decreases with the spatial distance as a power-law. A range parameter makes possible to cover the two limiting cases of local (nearest-neighbor) and a global (all-to-all) couplings. We consider an example from a non-linear auto-catalytic reaction-diffusion model.