Robert Mettin: abstract HOM

Chaotic Attractors from Homotopic Mixing of Vector Fields

Robert Mettin

Institut für Angewandte Physik, Technische Hochschule Darmstadt
Schloßgartenstraße 7, D-64289 Darmstadt, Germany

Gottfried Mayer-Kress

Center for Complex Systems Research, Department of Physics, Beckman Institute
University of Illinois at Urbana Champaign, Urbana, IL 61801, USA


We introduce homotopy transformations of vector fields as an efficient way to design families of chaotic attractors or transients with specific geometrical and dynamical properties. Those properties are inherited from different progenitor attractors, which allows a morphing between the progenitors. The method can provide a simple tool for a systematic design of attractors of desired dynamical characeristics. It is based on the robustnes of invariant manifolds of the homotopic vector fields with respect to parametric perturbations. We analytically construct a convex sub-family of Chua attractors which illustrates this approach. Connections to control and synchronization schemes of chaotic systems are shown. We also discuss applications in the area of sound synthesis.

Int. J. Bifurcation and Chaos 6(2), 395-408 (1996).

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