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Prevalence of unstable attractors in networks of pulse-coupled oscillators

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/persons/resource/persons173689

Timme,  Marc
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

/persons/resource/persons173710

Wolf,  Fred
Research Group Theoretical Neurophysics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

/persons/resource/persons215420

Geisel,  Theo
Department of Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Timme, M., Wolf, F., & Geisel, T. (2002). Prevalence of unstable attractors in networks of pulse-coupled oscillators. Physical Review Letters, 89(15), 154105-1-154105-4.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-1747-A
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.