Stochastic penetration of smooth and fractal basin boundaries under noise excitation

DOI10.1080/02681119008806101zbMath0726.70020OpenAlexW2011809508MaRDI QIDQ3348479

J. M. T. Thompson, Mohamed S. Soliman

Publication date: 1990

Published in: Dynamics and Stability of Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02681119008806101

zbMATH Keywords

homoclinic tangencyescape processOptimal escapebasin bifurcationsescape of a sinusoidally driven oscillatorminimum forcing magnitudepatterns of attractorsmall-amplitude linear natural frequencystochastic integrity measuresuperimposed noise excitationuniversal cubic potential

Mathematics Subject Classification ID

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

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The dynamical integrity concept for interpreting/ predicting experimental behaviour: from macro- to nano-mechanics ⋮ Potentials and limits to basin stability estimation ⋮ Michael Thompson: his seminal contributions to nonlinear dynamics -- and beyond ⋮ Controllability for Systems with Slowly Varying Parameters

Cites Work

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• An examination of initial condition maps for the sinusoidally excited buckled beam modeled by the Duffing's equation
• Fractal control boundaries of driven oscillators and their relevance to safe engineering design
• Integrity measures quantifying the erosion of smooth and fractal basins of attraction
• Chaotic phenomena triggering the escape from a potential well
• Basin boundary metamorphoses in the canonical escape equation