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Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Dec;70(6 Pt 2):066202. Epub 2004 Dec 3.

Morphological transitions and bistability in Turing systems.

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  • 1Laboratory of Computational Engineering, Helsinki University of Technology, P.O. Box 9203, FIN-02015 HUT, Finland.


It is well known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures, or their combinations, are observed. In this paper we study transitions between these states in both two and three dimensions. First, we derive the regions of stability for different patterns using nonlinear bifurcation analysis. Then, we apply large scale computer simulations to analyze the pattern selection in a bistable system by studying the effect of parameter selection on morphological clustering and the appearance of topological defects. The method elaborated in this paper presents a probabilistic approach for studying pattern selection in a bistable reaction-diffusion system.

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