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Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators

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

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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;

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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). Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators. Physical Review Letters, 89(25): 258701, pp. 258701-1-258701-4.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0029-172F-2
Abstract
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is determined by a multitude of linear operators. We treat this multioperator problem exactly and show that for inhibitory interactions the synchronous state is stable, independent of the parameters and the network connectivity. In randomly connected networks with strong interactions this synchronous state, displaying regular dynamics, coexists with a balanced state exhibiting irregular dynamics. External signals may switch the network between qualitatively distinct states.