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Dynamical stabilization of an unstable equilibrium in chemical and biological systems. (English) Zbl 1021.92026

Summary: The dynamics of two-component diffusion-reaction systems is considered. Using well-known models from population dynamics and chemical physics, it is shown that for certain parameter values the systems exhibit a rather unusual behaviour: a locally unstable equilibrium may become stable during a certain transition process. Both the analytical and numerical investigations of this phenomenon are presented in one and two spatial dimensions.

MSC:

92D25 Population dynamics (general)
92E20 Classical flows, reactions, etc. in chemistry
92D40 Ecology
35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
37N25 Dynamical systems in biology
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