Prevalence of unstable attractors in networks of pulse-coupled oscillators

Details Prevalence of unstable attractors in networks of pulse-coupled oscillators Prevalence of unstable attractors in networks of pulse-coupled oscillators

2002-02-25

arxiv.org/abs/cond-mat/0202438v2

Phys. Rev. Lett. 89:154105 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.89.154105

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are \textit{unstable}. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for large networks and a wide range of parameters. They are enclosed by basins of attraction of other attractors but are remote from their own basin volume such that arbitrarily small noise leads to a switching among attractors.

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