Domain Nucleation and Confinement In Agent Controlled Bistable Systems

TL;DR

This paper introduces a novel pattern formation mechanism in growing bistable systems with indirect coupling, where domains nucleate spontaneously at critical agent levels, differing from classical Turing patterns.

Contribution

It demonstrates a new domain nucleation and confinement mechanism in reaction-diffusion systems with non-diffusive activator and inhibitor molecules coupled via a fast diffusive agent.

Findings

Domains nucleate spontaneously at critical agent levels

Pattern formation differs from Turing's mechanism in monostable systems

Large domains can undergo wavenumber instability

Abstract

We report a new mechanism of pattern formation in growing bistable systems coupled indirectly. A modified Fujita et. al. model is studied as an example of a reaction-diffusion system of nondiffusive activator and inhibitor molecules immersed in the medium of a fast diffusive agent. Here we show that, as the system grows, a new domain nucleates spontaneously in the area where the local level of the agent becomes critical. Newly nucleated domains are stable and the pattern formation is different from Turing's mechanism in monostable systems. Domains are spatially confined by the agent even if the activator and inhibitor molecules diffuse. With the spatial extension of the system, a larger domain may undergo a wavenumber instability and the concentrations of active molecules within the neighboring elements of a domain can become sharply different. The new mechanism reported in this work can be generic for pattern formation systems involving multistability, growth, and indirect coupling.