Intermittency Driven By Band-limited Noise - the Inertial Regime

Nonlinear systems driven by band-limited noise exhibit intermittent dynamics over a wide frequency domain, as revealed by high-pass filtering the system response at a cut-on frequency much higher than the noise cut-off frequency. The statistics of the stationary intermittency thus developed is investigated in detail by analogue simulation of a simple monostable system, the overdamped quartic oscillator, in the limit of strong nonlinearity. The mathematical interpretation of our results is provided in terms of a statistically refined singular-perturbation argument, which explains the occurrence of an intermittent burst in the high-pass filtered signal with the close coincidence of a signal inflection point with a noise zero-crossing. Our interest focuses on a characteristic frequency domain, where the intermittent phenomenon is sensitive to the nonlinear nature of the system, only, irrespective of the driving noise statistics (inertial range).