Subcritical Turing bifurcation and the morphogenesis of localised patterns

TL;DR

This paper investigates how subcritical Turing bifurcations in reaction-diffusion systems naturally lead to the formation of stable, localized patterns through homoclinic snaking, with implications for physical phase transitions.

Contribution

It demonstrates that subcritical Turing bifurcations occur naturally in reaction-diffusion systems with source and loss effects, leading to robust localized pattern formation.

Findings

Subcritical bifurcations induce localized patterns via homoclinic snaking.

Balance of source and loss effects causes super/subcritical transitions.

Implications for physical systems with phase transitions to localized patterns.

Abstract

Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing source and loss effects are included in a typical reaction-diffusion system, leading to a super/subcritical transition. Implications are discussed for a range of physical problems, arguing that subcriticality leads to naturally robust phase transitions to localised patterns.