Coupled three-state oscillators

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.