Robustness of the Noise-Induced Phase Synchronization in a General Class of Limit Cycle Oscillators

We show that a wide class of uncoupled limit-cycle oscillators can be in-phase synchronized by common weak additive noise. An expression of the Lyapunov exponent is analytically derived to study the stability of the noise-driven synchronizing state. The result shows that such a synchronization can be achieved in a broad class of oscillators with little constraint on their intrinsic property. On the other hand, the leaky integrate-and-fire neuron...