Stochastic penetration of smooth and fractal basin boundaries under noise excitation

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Abstract
Recent work on the escape of a sinusoidally driven oscillator from a universal cubic potential well has elucidated the complex patterns of attractor and basin bifurcations that govern the escape process. Optimal escape, under a minimum forcing magnitude, occurs at a forcing frequency of about 80 per cent of the small-amplitude linear natural frequency, and at this forcing frequency we have identified a significant and dramatic erosion of the safe basin of attraction, triggered by a homoclinic tangency, that would seriously impair the engineering integrity of a practical system long before the final chaotic instability of the constrained attractor. Introducing a superimposed noise excitation, we here quantify this in terms of a stochastic integrity measure, and correlate this with the geometric changes experienced by the deterministic basin of attraction