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.

arXiv comment6 pages, 4 figures

References in corpus (4)

• Snakes and ladders: localized solutions of plane Couette flow
• Dynamics and pattern formation in invasive tumor growth
• The formation of labyrinths, spots and stripe patterns in a biochemical approach to cardiovascular calcification
• Front motion and localized states in an asymmetric bistable activator-inhibitor system with saturation

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