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Melnikov Processes and Noise-Induced Escapes: Applications to Engineering, Physics, and Biology.


pdf icon Melnikov Processes and Noise-Induced Escapes: Applications to Engineering, Physics, and Biology. (1710 K)
Franaszek, M.; Frey, M. R.; Simiu, E.

Stochastically Excited Nonlinear Ocean Structures. Chapter 7, World Scientific, NJ, Shlesinger, M. F.; Swean, T., Editor(s)(s), 187-212 pp, 1998.

Keywords:

building technology; chaos; dynamical systems; Melnikov processes; multistable systems; structural engineering

Abstract:

For a class of deterministic systems the necessary condition for chaos is that the system's Melnikov function have simple zeros. The behavior of those systems' stochastic counterparts is similarly characterized by their Melnikov processes. We summarize: (1) recent research by the authors on the use of Melnikov processes to obtain weak upper bounds for rates of escape from a potential wall induced by a variety of types of noise, including dichotomous noise, and (2) applications of Melnikov processes in oceanography, the investigation of column snap-through induced by stochastic loads, nonlinear control, stochastic resonance, and the behavior of auditory nerve fibers.