Intermittent Behavior and Synchronization of Two Coupled Noisy Driven Oscillators

The coupled system of two forced Liénard-type oscillators has applications in diode-based electric circuits and phenomenological models for the heartbeat. These systems typically exhibit intermittent transitions between laminar and chaotic states; what affects their performance and, since noise is always present in such systems, dynamical models should include these effects. Accordingly, we investigated numerically the effect of noise in two intermittent phenomena: the intermittent transition to synchronized behavior for identical and unidirectionally coupled oscillators, and the intermittent transition to chaos near a periodic window of bidirectionally coupled oscillators. We found that the transition from a nonsynchronized to a synchronized state exhibits a power-law scaling with exponent 3/2 characterizing on-off intermittency. The inclusion of noise adds an exponential tail to this scaling.