Subcritical Turing bifurcation and the morphogenesis of localized patterns.

Area of Science:

• Mathematical modeling
• Physical chemistry
• Nonlinear dynamics

Background:

• Reaction-diffusion systems are fundamental to modeling spatially extended phenomena.
• Turing bifurcations typically describe pattern formation.
• Homoclinic snaking is a known mechanism for localized structures.

Purpose of the Study:

• Investigate subcritical Turing bifurcations in large domains.
• Explain the spontaneous onset of localized patterns.
• Explore the role of source-loss balance in pattern formation.

Main Methods:

• Analysis of reaction-diffusion systems.
• Study of homoclinic snaking mechanism.
• Mathematical modeling of super- to subcritical transitions.

Main Results:

• Subcritical Turing bifurcations naturally occur in large domains.
• Homoclinic snaking drives the formation of well-developed localized patterns.
• Balancing source and loss effects induces a super- to subcritical transition.

Conclusions:

• Subcriticality provides a mechanism for robust phase transitions to localized patterns.
• The findings have implications for various physical problems.
• Localized patterns can arise spontaneously under specific conditions.