Correlation resonance in noise-driven coupled nonlinear oscillators

Mutual correlation between a pair of coupled limit-cycle oscillators driven by external noise is analytically and numerically studied under the assumption that those oscillators are nearly identical and weakly coupled so that phase reduction is possible. For such a case that the oscillators cannot entrain each other in the absence of noise, the correlation is enhanced by noise in a range of its intensity starting from zero and then enfeebled beyond that range. This resonance-like phenomenon, named correlation resonance, is theoretically explained and then demonstrated for coupled time-dependent Ginzburg-Landau equations, coupled Brusselators, and coupled Mackey-Glass equations as examples. All these results suggest that the resonance is a fairly robust phenomenon. The case of mutually entrained oscillators is also discussed.