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The bifurcation diagram of a model chemical reaction—II. Two dimensional time-periodic patterns

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Abstract

The bifurcation equations of a general reaction-diffusion system are derived for a circular surface. Particular attention is directed to the deformation of the circular boundary into an elliptic shape. This leads to a new bifurcation diagram which may involve secondary bifurcation, but which retains however the basic characteristics of the solutions for the circular case. Numerical simulations of the various coexisting, time-periodic and space-dependent solutions, are presented for a simple model reaction and circular geometry.

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Authors and Affiliations

  1. Faculté des Sciences, Université Libre de Bruxelles, Chimie-physique II, Campus plaine C.P.231, Boulevard du Triomphe, 1050, Bruxelles, Belgium

    T. Erneux & M. Herschkowitz-Kaufman

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  1. T. Erneux
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  2. M. Herschkowitz-Kaufman
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Erneux, T., Herschkowitz-Kaufman, M. The bifurcation diagram of a model chemical reaction—II. Two dimensional time-periodic patterns. Bltn Mathcal Biology 41, 767–790 (1979). https://doi.org/10.1007/BF02462375

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  • DOI: https://doi.org/10.1007/BF02462375

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