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Published on: September 26, 2016
Instability and pattern formation in reaction-diffusion systems: a higher order analysis
Syed Shahed Riaz1, Rahul Sharma, S P Bhattacharyya
1Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India.
Abstract:
We analyze the condition for instability and pattern formation in reaction-diffusion systems beyond the usual linear regime. The approach is based on taking into account perturbations of higher orders. Our analysis reveals that nonlinearity present in the system can be instrumental in determining the stability of a system, even to the extent of destabilizing one in a linearly stable parameter regime. The analysis is also successful to account for the observed effect of additive noise in modifying the instability threshold of a system. The analytical study is corroborated by numerical simulation in a standard reaction-diffusion system.
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