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Prevalence of unstable attractors in networks of pulse-coupled oscillators

Marc Timme·Fred Wolf·Theo Geisel
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Abstract

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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Marc Timme, Fred Wolf, Theo Geisel. 2002-10-01. Prevalence of unstable attractors in networks of pulse-coupled oscillators. https://doi.org/10.1103/physrevlett.89.154105

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