Influence of physical interactions on spatiotemporal patterns

TL;DR

This paper investigates how physical interactions influence spatiotemporal patterns in cyclic reactions, revealing that such interactions significantly alter pattern dynamics and could impact biodiversity in ecological systems.

Contribution

It extends reaction-diffusion models by incorporating physical interactions, showing their effects on pattern formation and dynamics in cyclic dominant reactions.

Findings

Weak interactions modify spiral wave scales

Strong repulsive interactions create oscillating lattices

Attractive interactions lead to phase separation and co-located oscillations

Abstract

Spatiotemporal patterns are often modeled using reaction-diffusion equations, which combine complex reactions between constituents with ideal diffusive motion. Such descriptions neglect physical interactions between constituents, which might affect resulting patterns. To overcome this, we study how physical interactions affect cyclic dominant reactions, like the seminal rock-paper-scissors game, which exhibits spiral waves for ideal diffusion. Generalizing diffusion to incorporate physical interactions, we find that weak interactions change the length- and time-scales of spiral waves, consistent with a mapping to the complex Ginzburg-Landau equation. In contrast, strong repulsive interactions typically generate oscillating lattices, and strong attraction leads to an interplay of phase separation and chemical oscillations, like droplets co-locating with cores of spiral waves. Our work suggests that physical interactions are relevant for forming spatiotemporal patterns in nature, and it might shed light on how biodiversity is maintained in ecological settings.