The metastable states in the system of coupled bistable elements:
three approaches to mean escape time estimation
A.V. Polovinkin
University of Nizhny Novgorod, Russia
The system of coupled bistable elements under small noise influence, simu-lating many physical phenomena is considered. The mean escape times from metastable states with and without stochastic synchronizationlike behavior of elements are investigated.
It is shown, that the mean living time estimated from the well-known classical expression for the escape rate leads to physically incorrect results (approaching zero or infinity) when the coupling parameter tends to the bifurcation values.
The numerical simulation of stochastic differential equations shows, that the classical formula for mean escape time is in good agreement with the numerical results only far from bifurcation parameter values, i.e. for big or for extremely small (near the zero) coupling parameter values.
Employing analytical results, obtained by Matkowsky and Schuss the new asymptotic expression for mean escape times from the metastable state is derived, which have much better agreement with simulation date, than classical expression.
It is shown, that proposed expression:
-leads to the classical mean-time formula in the case of rigorously parabolic dependence of potential near the metastable and saddle points,
-can be worked out analytically in some interesting non-parabolic special cases,
-and can be represented as the combination of solutions of ordinary differential equations in general case. pt