CHAOTIC ATTRACTORS FROM HOMOTOPIC MIXING OF VECTOR FIELDS
Robert Mettin, Gottfried Mayer‐Kress · International Journal of Bifurcation and Chaos · 1996
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 characteristics. It is based on the robustness of invariant manifolds of the homotopic vector fields with respect to parametric perturbations. We analytically construct a convex subfamily of Chua attractors which illustrates this approach. Connections to control and synchronisation schemes of chaotic systems are shown. We also discuss applications in the area of sound synthesis.