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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.

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