New Tool for the Investigation of a Class of Nonlinear Stochastic Differential Equations: The Melnikov Process.
New Tool for the Investigation of a Class of Nonlinear
Stochastic Differential Equations: The Melnikov
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
building technology; chaotic dynamics; control theory;
nonlinear dynamics; oceanography; stochastic
differential equations; structural engineering
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