Reliable and unreliable dynamics in driven coupled oscillators

This letter concerns the reliability of coupled oscillator networks in response to fluctuating inputs. Reliability means that (following a transient) an input elicits identical responses upon repeated presentations, regardless of the system's initial condition. Here, we analyze this property for two coupled oscillators, demonstrating that oscillator networks exhibit both reliable and unreliable dynamics for broad ranges of coupling strengths. We further argue that unreliable dynamics are characterized by strange attractors with random SRB measures, implying that though unreliable, the responses lie on low-dimensional sets. Finally, we show that 1:1 phase locking in the zero-input system corresponds to high susceptibility for unreliable responses. A geometric explanation is proposed.