Ira B. Schwartz, Thomas W. Carr, Lora Billings, Mark Dykman
We consider the problem of switching in stochastic systems with delayed feedback. A general variational formulation is derived for the switching rate in a stochastic differential delay equation where the noise source is of general form. The resulting equations of motion and boundary conditions describe the optimal escape path which maximizes the probability of escape. Analyzing the dynamics along the optimal path yields exponents of the distribution in terms of delay time, dissipation, and noise intensity. Theoretical predictions compare very well with numerical simulations in both additive and multiplicative noise cases, even outside of regions where the delay is assumed to be small. Manuscript approved
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http://arxiv.org/abs/1207.7278
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