Abstract
We study the post-critical behavior of a perturbed bistable Hamiltonian system to which the Melnikov approach is applicable under the assumption that the perturbation is asymptotically small. We examine the case of perturbations that are sufficiently large to cause chaotic transport between phase space regions associated with the system's potential wells. The main results are: (1) a small additional harmonic excitation can cause substantial changes in the system's mean residence time, and (2) the dependence of the magnitude of these changes on the additional excitation's frequency is similar to the dependence on frequency of the system's Melnikov scale factor. We discuss the relevance of these results to the design of efficient, Melnikov-based open loop controls aimed at increasing the mean residence time for the stochastically excited counterpart of the system.
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