Robert Mettin: abstract HOM
Chaotic Attractors from Homotopic Mixing of Vector Fields
Institut für Angewandte Physik, Technische Hochschule Darmstadt
Schloßgartenstraße 7, D-64289 Darmstadt, Germany
Center for Complex Systems Research,
Department of Physics, Beckman Institute
University of Illinois at Urbana Champaign, Urbana, IL 61801,
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).