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

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

2002-07-12

arxiv.org/abs/cond-mat/0207313v2

Phys. Rev. Lett. 89, 258701 (2002)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.89.258701

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 multi-operator problem analytically 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 \textit{regular} dynamics, coexists with a balanced state that exhibits \textit{irregular} dynamics such that external signals may switch the network between qualitatively distinct states.

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