Peeling Bifurcations of Toroidal Chaotic Attractors

Details Peeling Bifurcations of Toroidal Chaotic Attractors Peeling Bifurcations of Toroidal Chaotic Attractors

2007-07-26

arxiv.org/abs/0707.3975v3

Nonlinear Sciences

Chaotic Dynamics

7 pages, 14 figures, accepted to Physical Review E

Scientific paper

10.1103/PhysRevE.76.066204

Chaotic attractors with toroidal topology (van der Pol attractor) have counterparts with symmetry that exhibit unfamiliar phenomena. We investigate double covers of toroidal attractors, discuss changes in their morphology under correlated peeling bifurcations, describe their topological structures and the changes undergone as a symmetry axis crosses the original attractor, and indicate how the symbol name of a trajectory in the original lifts to one in the cover. Covering orbits are described using a powerful synthesis of kneading theory with refinements of the circle map. These methods are applied to a simple version of the van der Pol oscillator.

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