Intermediate physical interactions induce spatiotemporal dynamics in Turing patterns

TL;DR

This paper explores how physical interactions in reaction-diffusion systems can lead to complex, dynamic Turing patterns exhibiting chaos, coarsening, and fission, expanding understanding of pattern formation beyond classical models.

Contribution

It demonstrates that physical interactions can induce chaotic and dynamic Turing patterns, revealing three distinct regimes in reaction-diffusion systems with physical interactions.

Findings

Physical interactions can promote or induce chaotic patterns.

Patterns exhibit cycles of droplet coarsening and fission.

Three distinct regimes emerge from nonlinear reactions and physical interactions.

Abstract

Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at different rates and reactions are sufficiently nonlinear. However, real systems are more complex and particularly involve physical interactions between constituents. While such interactions can promote patterns, we here show that they can also induce dynamic, chaotic patterns. These patterns exhibit well-defined length and time scales, which result from cycles of droplet coarsening and fission. The dynamical patterns combine properties of traditional Turing patterns and chemically active droplets, which emerge for strong physical interactions. Our analysis thus reveals three qualitatively different regimes that emerge when two components interact physically and undergo nonlinear reactions.