Synchronization regimes in coupled noisy excitable systems

We study synchronization regimes in a system of two coupled noisy excitable systems which exhibit excitability close to an Andronov bifurcation. The uncoupled system possesses three fixed points: a node, a saddle, and an unstable focus. We demonstrate that with an increase of coupling strength the system undergoes transitions from a desynchronous state to a train synchronization regime to a phase synchronization regime, and then to a complete synchronization regime. Train synchronization is a consequence of the existence of a saddle in the phase space. The mechanism of transitions in coupled noisy excitable systems is different from that in coupled phase-coherent chaotic systems.