Characterization of spatiotemporal chaos in an inhomogeneous active medium

TL;DR

This paper investigates spatiotemporal chaos in an inhomogeneous reaction-diffusion system, analyzing unstable periodic orbits and their topological properties to understand the underlying chaotic dynamics.

Contribution

It introduces a method to analyze the topological structure of unstable orbits in inhomogeneous active media using bi-orthogonal decomposition.

Findings

Unstable periodic orbits can be embedded in three dimensions.

A minimal number of modes necessary to capture the chaotic organization.

Topological properties of chaos in inhomogeneous media are characterized.

Abstract

We study a reaction diffusion system of the activator-inhibitor type with inhomogeneous reaction terms showing spatiotemporal chaos. We analyze the topological properties of the unstable periodic orbits in the slow chaotic dynamics appearing, which can be embedded in three dimensions. We perform a bi-orthogonal decomposition analyzing the minimum number of modes necessary to find the same organization of unstable orbits.