Quasi-threshold phenomenon in noise-driven Higgins model

Abstract

The quasi-threshold phenomenon in Higgins model with mono-stability driven by Gaussian white noise is investigated. The initial excitation phase is identified as escaping event with a specific trajectory defined as the quasi-threshold. In the limit of weak noise, a group of differential equations governing the optimal exit path, quasi-potential and exponential prefactor are deduced via WKB approximation. Results show that the optimal path approaches the quasi-threshold with a nearly tangent way and almost follows the deterministic flow subsequently in the quasi-potential plateau, making it analogous to the bistable system. Numerical experiments verify not only the results of the optimal path but also the ones of the optimal fluctuational forces. Then the difference between the practical exit location and the position with minimal quasi-potential is also revealed by including the exponential prefactor into the expression of exit location distribution. Finally, the mean first passage time (MFPT) is evaluated theoretically with the secondary-order-approximation taken into consideration. These findings and computations shed light on exploring underlying qualitative mechanism and quantitative feature of excitation behaviors in biological systems.