The use of Melnikov processes for the identification of a class of multistable systems

Abstract

We review briefly basic Melnikov theory for both deterministic and stochastic systems. We then show how the theory can be used for the identification of a class of multistable systems for which experimental data are available on the relation between excitation frequency and rate of escape from a potential well. We illustrate our approach for the case of the auditory nerve fiber, for which the use of Melnikov theory yields a model that provides a transparent phenomenological description of the system behavior, and performs considermerelably better than the the classical Fitzhugh-Nagumo equation.