Subcritical Turing bifurcation and the morphogenesis of localised 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.