Periodic solutions of an autonomous reaction-diffusion system - A model system

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. © 2001 Plenum Publishing Corporation.