Prevalence of unstable attractors in networks of pulse-coupled oscillators
Marc Timme, Fred Wolf, Theo Geisel
Abstract
We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are 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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