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Periodic Solutions of an Autonomous Reaction-Diffusion System—A Model System

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Abstract

We describe the dynamics of an autonomous system of two reaction-diffusion equations which can be looked at as a model system for more general reaction-diffusion systems. In our system all solutions tend to zero or to (finitely many) periodic orbits which can be fully described—including their stability properties. Furthermore, we construct invariant sets for the period map and show how a new invariant called torsion number is related to our model system.

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  1. Mathematisches Institut, Justus-Liebig-Universität Gießen, Gießen, Germany

    Matthias Büger

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  1. Matthias Büger
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Büger, M. Periodic Solutions of an Autonomous Reaction-Diffusion System—A Model System. Journal of Dynamics and Differential Equations 13, 589–612 (2001). https://doi.org/10.1023/A:1016686323983

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