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Stochastic penetration of smooth and fractal basin boundaries under noise excitation. (English) Zbl 0726.70020

(Authors’ summary:) 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.
Reviewer: P.Smith (Keele)

MSC:

70K50 Bifurcations and instability for nonlinear problems in mechanics
34C23 Bifurcation theory for ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
70L05 Random vibrations in mechanics of particles and systems
34C25 Periodic solutions to ordinary differential equations
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References:

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