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

@article{Timme2002CoexistenceOR,
  title={Coexistence of regular and irregular dynamics in complex networks of pulse-coupled oscillators.},
  author={Marc Timme and Fred R. Wolf and Theo Geisel},
  journal={Physical review letters},
  year={2002},
  volume={89 25},
  pages={258701}
}
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… CONTINUE READING

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