Change of the Most Probable Escape Path in a Fast-Slow Insect Outbreak System Under Different Noise Amplitude Ratios

Abstract

Noise-induced escape from the domain of attraction of a stable state in a fast-slow insect outbreak system is investigated. According to Dannenberg's theory (et al., 2014, “Steering Most Probable Escape Paths by Varying Relative Noise Intensities,” Phys. Rev. Lett., 113(2), p. 020601), only noise amplitude ratio μ will lead to the change of the most probable escape path (MPEP). Therefore, the research emphasis of this paper is to extend their study and discuss the variation of the MPEP in more detail. First, for the case of μ = 1, the MPEP almost moves along the critical manifold. Via projecting the full system onto the critical manifold, a reduced system is obtained, and the action of the MPEP in the full system can be partly evaluated by that in the reduced system. In order to test the accuracy of the computed MPEP, based on the iterative action minimizing method (IAMM), a new relaxation method, which can reduce the central processing unit time, is then presented. Then, as μ converges to zero, an improved analytical method is given, through which a better approximation for the MPEP at the turning point is obtained. And then, when the value of μ is moderate, the MPEP will peel off the critical manifold. To determine the changing point on the critical manifold, an effective numerical algorithm is presented. In brief, a complete investigation on the structural change of the MPEP in a fast-slow insect outbreak system under different noise ratios is given, and the results of the numerical simulation match well with the analytical ones.