Noise-induced breakdown of stochastic resonant behavior of van der Pol oscillators coupled by time-varying resistor

We explore the behavior of two van der Pol oscillators coupled by a stochastically time-varying resistor. We observe switching between in-phase and anti-phase synchronization and analyze the statistics of the switching, with and without additional noise. We find stochastic resonant behavior of synchronization in both regimes. Correlating the two noise sources quickly destroys the stochastic resonance phenomenon in the anti-phase synchronization regime. In the in-phase regime, noise correlation first contributes to the synchronization before removing the resonance by taking over the synchronization by its own means.