Melnikov Processes and Noise-Induced Escapes: Applications to Engineering, Physics, and Biology.
Melnikov Processes and Noise-Induced Escapes:
Applications to Engineering, Physics, and Biology.
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.
building technology; chaos; dynamical systems; Melnikov
processes; multistable systems; structural engineering
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