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arXiv · 1104.3023

Delay induced bifurcation of dominant transition pathways

Huijun Jiang·Zhonghuai Hou
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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 $\tau$ 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 $\tau-\beta$ plane, where $\beta$ measures the non-conservation of the original Maier-Stein model.

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Huijun Jiang, Zhonghuai Hou. 2011-04-15. Delay induced bifurcation of dominant transition pathways. https://doi.org/10.1063/1.4749795

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