Prevalence of unstable attractors in networks of pulse-coupled oscillators |
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Authors: | Timme Marc Wolf Fred Geisel Theo |
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Affiliation: | Max-Planck-Institut für Str?mungsforschung and Fakult?t für Physik, Universit?t G?ttingen, Germany. |
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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, and become prevalent with increasing network size for 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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