Dynamics of Cyclic Feedback Systems
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The dynamics of cyclic feedback systems are described. The emphasis is both in showing the diversity of possible dynamics in these systems and in showing that there is a underlying dynamic structure possessed by all these systems. In particular, for the special class of monotone cyclic feedback systems, the dynamics is fairly simple; the recurrent sets can only consist of fixed points or periodic orbits and in many cases can be shown to be Morse-Smale. This is contrasted with the general cyclic feedback systems for which chaotic dynamics can occur. The general properties which large subclasses of these systems have in common include periodic orbits and a semi-conjugacy onto a simple, non-trivial, model dynamical system. To describe all systems simultaneously, a purely topological description of the invariant sets is introduced.