Delay induced bifurcation of dominant transition pathways

Abstract

We investigate delay effects on dominant transition pathways (DTP) between metastable states of stochastic systems. A modified version of the Maier-Stein model with linear delayed feedback is considered as an example. By a stability analysis of the "on-axis" DTP in trajectory space, we find that a bifurcation of DTPs will be induced when time delay τ is large enough. This finding is soon verified by numerically derived DTPs which are calculated by employing a recently developed minimum action method extended to delayed stochastic systems. Further simulation shows that the delay-induced bifurcation of DTPs also results in a nontrivial dependence of the transition rate constant on the delay time. Finally, the bifurcation diagram is given on the τ-β plane, where β measures the non-conservation of the original Maier-Stein model.