  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.
