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Chaos as a limit in a boundary value problem. (English) Zbl 0588.58046
A piecewise-linear, 3-variable autonomous O.D.E. of $$C^ 0$$ type, known to describe constant-shape traveling waves in one-dimensional reaction- diffusion media of Rinzel-Keller type, is numerically shown to possess a chaotic attractor in state space. An analytical method proving the possibility of chaos is outlined and a set of parameters yielding Shil’nikov chaos indicated. A symbolic dynamics technique can be used to show how the limiting chaos dominates the behavior even of the finite boundary value problem.

##### MSC:
 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior