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Coupled three-state oscillators

T. Prager·B. Naundorf·L. Schimansky-Geier
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Abstract

We investigate globally coupled stochastic three-state oscillators, which we consider as general models of stochastic excitable systems. We compare two situations:in the first case the transitions between the three states of each unit 1->2->3->1 are determined by Poissonian waiting time distributions. In the second case only transition 1->2 is Poissonian whereas the others are deterministic with a fixed delay. When coupled the second system shows coherent oscillations whereas the first remains in a stable stationary state. We show that the coherent oscillations are due to a Hopf-bifurcation in the dynamics of the occupation probabilities of the discrete states and discuss the bifurcation diagram.

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T. Prager, B. Naundorf, L. Schimansky-Geier. 2002-11-14. Coupled three-state oscillators. https://doi.org/10.1016/s0378-4371(03)00196-1

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