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Phys Rev Lett. 2002 Dec 16;89(25):258701. Epub 2002 Nov 27.

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

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Max-Planck-Institut für Strömungsforschung and Fakultät für Physik, Universität Göttingen, Germany.


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.

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