Delay induced bifurcation of dominant transition pathway

Details Delay induced bifurcation of dominant transition pathway Delay induced bifurcation of dominant transition pathway

2011-04-15

arxiv.org/abs/1104.3023v2

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5 pages, 5 figures

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The dominant transition pathway (DTP) is informative to explain the mechanism of fluctuation-driven transitions, such as chemical reactions, biological switches, nucleation processes. In the present paper, we investigate the DTP between two metastable states in a delayed stochastic system. A modified version of the Maier-Stein model with linear delayed feedback is considered as an example. By an analysis using small delay approximation, we find that time delay induce a new DTP via a bifurcation in trajectory space. This finding is verified by numerically derived DTPs which are calculated by employing a recently developed minimum action method extended to delayed stochastic systems. Furthermore, the delay-induced bifurcation in trajectory space results in a nontrivial dependence of the transition probability on the delay time.

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