A New Tool for the Investigation of a Class of Nonlinear Stochastic Differential Equations: the Melnikov Process
The Melnikov process, a construct rooted in chaotic dynamics theory, was recently developed as a tool for the investigation of a broad class of nonlinear stochastic differential equations [1–6]. This paper briefly reviews the stochastic Melnikov-based approach and applications to (i) oceanography, (ii) open-loop control of stochastic nonlinear systems, and (iii) snap-through of buckled beams with distributed mass and distributed random loading.
KeywordsControl Force Unstable Manifold Homoclinic Orbit Escape Rate Melnikov Function
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