Escape rates in periodically driven Markov processes |
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Institution: | 1. Faculty of Science, Kunming University of Science and Technology, Kunming 650500, China;2. College of Physics and Information Engineering, Zhaotong University, Zhaotong 657000, China;1. Institute of Physics, University of Silesia, 40-007 Katowice, Poland;2. Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland |
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Abstract: | We present an approximate analytical expression for escape rates of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is based on a discrete state Markovian modeling of the full long-time dynamics with time-dependent rates. It is valid in a wide parameter regime beyond the restraining limits of weak driving (linear response) and/or weak noise. The scheme is carefully tested and yields excellent agreement with three different numerical methods based on the Langevin equation, the Fokker–Planck equation and an integral equation. |
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