ar X iv : 0 71 2 . 03 35 v 1 [ nl in . C D ] 3 D ec 2 00 7 Excitable systems with noise and delay with applications to control : renewal theory approach
نویسنده
چکیده
We present an approach for the analytical treatment of excitable systems with noise-induced dynamics in the presence of time delay. An excitable system is modeled as a bistable system with a time delay, while another delay enters as a control term taken after [Pyragas 1992] as a difference between the current system state and its state τ time units before. This approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term.
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