American Institute of Physics, Chaos: An Interdisciplinary Journal of Nonlinear Science, 3(22), p. 033141
DOI: 10.1063/1.4749795
Full text: Download
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. ; Comment: 14 pages, 6 figures