Competitively Coupled Maps and Spatial Pattern Formation

TL;DR

This paper introduces a simple, robust coupled map lattice model with competitive interactions that spontaneously breaks symmetry and forms stable spatial patterns across various geometries, offering an alternative to traditional reaction-diffusion models.

Contribution

It presents a novel coupled map lattice model with competitive coupling, providing a robust mechanism for pattern formation that differs from traditional diffusive models.

Findings

Competitive coupling induces spontaneous symmetry breaking.

Stable spatial patterns form across diverse geometries.

Pattern formation occurs even with trivial local dynamics.

Abstract

Spatial pattern formation is a key feature of many natural systems in physics, chemistry and biology. The essential theoretical issue in understanding pattern formation is to explain how a spatially homogeneous initial state can undergo spontaneous symmetry breaking leading to a stable spatial pattern. This problem is most commonly studied using partial differential equations to model a reaction-diffusion system of the type introduced by Turing. We report here on a much simpler and more robust model of spatial pattern formation, which is formulated as a novel type of coupled map lattice. In our model, the local site dynamics are coupled through a competitive, rather than diffusive, interaction. Depending only on the strength of the interaction, this competitive coupling results in spontaneous symmetry breaking of a homogeneous initial configuration and the formation of stable spatial patterns. This mechanism is very robust and produces stable pattern formation for a wide variety of spatial geometries, even when the local site dynamics is trivial.