Turing pattern formation in heterogeneous media

Abstract The effects of spatial inhomogeneities in the initial distribution of immobile complexing species on the spatiotemporal dynamics of activator-inhibitor systems are investigated. If the initial concentration of the complexing species is below a critical value and homogeneously distributed, the stable attractor is a limit cycle; for higher concentrations the stable attractor is a Turing pattern. When the complexing agent is inhomogeneously distributed interactions between the oscillatory dynamics and Turing pattern formation are possible. Such phenomena are investigated in a model system, the Sel'kov model with a complexing reaction. The effects of the symmetries and lengths that characterize the initial distribution of complexing agent on the spatiotemporal attracting states are studied. The study provides insight into the types of behavior that are possible in heterogeneous media undergoing Turing-like bifurcations.

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