Dynamics of excitable elements with time-delayed coupling

Motivated by recent experiments on intracellular calcium release we study the effects of different types of coupling on the dynamics of arrays of excitable elements. We intend to find a mechanism that produces a sustained activity of the elements following a spike. While instantaneous diffusive coupling does not exhibit this property, we show that, for a coupling term with temporal delay, signals from adjacent elements can serve as mutual excitations and thus prolong the duration of the signal. We propose that time delayed coupling is generated by diffusion between isolated clusters of calcium channels. Our model could thus provide an explanation for two different release modes observed in the Ca2+Ca2+ system.