Noise-dependent stability of the synchronized state in a coupled system of active rotators

We consider a Kuramoto model for the dynamics of an excitable system consisting of two coupled active rotators. Depending on both the coupling strength and the noise, the two rotators can be in a synchronized or desynchronized state. The synchronized state of the system is most stable for intermediate noise intensity in the sense that the coupling strength required to desynchronize the system is maximal at this noise level. We evaluate the phase boundary between synchronized and desynchronized states through numerical and analytical calculations.