Strange attractors in periodically-kicked degenerate Hopf bifurcations

Details Strange attractors in periodically-kicked degenerate Hopf bifurcations Strange attractors in periodically-kicked degenerate Hopf bifurcations

2007-06-15

arxiv.org/abs/0706.2370v1

Mathematics

Dynamical Systems

16 pages

Scientific paper

10.1007/s00220-008-0499-0

We prove that spiral sinks (stable foci of vector fields) can be transformed into strange attractors exhibiting sustained, observable chaos if subjected to periodic pulsatile forcing. We show that this phenomenon occurs in the context of periodically-kicked degenerate supercritical Hopf bifurcations. The results and their proofs make use of a new multi-parameter version of the theory of rank one maps developed by Wang and Young.

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