Bifurcation From Networks of Unstable Attractors to Heteroclinic Switching

Details Bifurcation From Networks of Unstable Attractors to Heteroclinic Switching Bifurcation From Networks of Unstable Attractors to Heteroclinic Switching

2007-09-21

arxiv.org/abs/0709.3432v2

C. Kirst and M. Timme, Phys. Rev. E 065201(R) (2008)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 Figures

Scientific paper

10.1103/PhysRevE.78.065201

We present a dynamical system that naturally exhibits two unstable attractors that are completely enclosed by each others basin volume. This counter-intuitive phenomenon occurs in networks of pulse-coupled oscillators with delayed interactions. We analytically and numerically investigate this phenomenon and clarify the mechanism underlying it: Upon continuously removing the non-invertibility of the system, the set of two unstable attractors becomes a set of two non-attracting saddle states that are heteroclinically connected to each other. This transition from a network of unstable attractors to a heteroclinic cycle constitutes a new type of bifurcation in dynamical systems.

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