Statistical distribution and stochastic resonance in a periodically driven chemical system

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Abstract
The probability density distribution is studied analytically and by Monte Carlo simulations for a periodically driven chemical bistable system, described by a master equation, for the case of low‐frequency driving. The quasistationary distribution about the stable states is well approximated by the solution of the master equation in the eikonal approximation for large volumes of the system. For a one‐component system both the exponent and the prefactor of the steady distribution are obtained in explicit form, for an arbitrary strength of the driving and for an arbitrary interrelation between the frequency of the driving and the probabilities of transitions between the stable states. The results of the simulations are in good agreement with analytical results. We demonstrate the onset of stochastic resonance for the driving frequency close to the probabilities of fluctuational transitions between the states.

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