A New Tool for the Investigation of a Class of Nonlinear Stochastic Differential Equations: the Melnikov Process

  • E. Simiu
  • M. Franaszek
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)


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.


Control Force Unstable Manifold Homoclinic Orbit Escape Rate Melnikov Function 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • E. Simiu
    • 1
  • M. Franaszek
    • 1
  1. 1.National Institute of Standards and TechnologyGaithersburgUSA

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