Kahlert, Claus; Rössler, Otto E. Chaos as a limit in a boundary value problem. (English) Zbl 0588.58046 Z. Naturforsch. A 39, 1200-1203 (1984). 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. Cited in 1 Document MSC: 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:reaction-diffusion media of Rinzel-Keller type; Shil’nikov chaos; symbolic dynamics; limiting chaos PDF BibTeX XML Cite \textit{C. Kahlert} and \textit{O. E. Rössler}, Z. Naturforsch., A 39, 1200--1203 (1984; Zbl 0588.58046)