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


pdf icon New Tool for the Investigation of a Class of Nonlinear Stochastic Differential Equations: The Melnikov Process. (484 K)
Simiu, E.; Franaszek, M.

Advances in Nonlinear Stochastic Mechanics IUTAM Symposium. Proceedings. July 3-7, 1995, Trondheim, Norway, Kluwer Academic Publishers, Boston, MA, Naess, A.; Krenk, S., Editor(s)(s), 427-463 pp, 1996.

Sponsor:

Office of Naval Research, Arlington, VA

Keywords:

building technology; chaotic dynamics; control theory; nonlinear dynamics; oceanography; stochastic differential equations; structural engineering

Abstract:

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. This paper briefly reviews the stochastic Melnikov-based approach and applications to (1) oceanography, (2) open-loop control of stochastic nonlinear systems and (3) snap-through of buckled beams with distributed mass and distributed random loading.