Noise-intensity fluctuation in Langevin model and its higher-order Fokker-Planck equation

Details Noise-intensity fluctuation in Langevin model and its higher-order Fokker-Planck equation Noise-intensity fluctuation in Langevin model and its higher-order Fokker-Planck equation

2010-04-08

arxiv.org/abs/1004.1252v4

Physica A 390, 1051 (2011)

Physics

Condensed Matter

Statistical Mechanics

23 pages, 7 figures, 1 table

Scientific paper

10.1016/j.physa.2010.11.007

In this paper, we investigate a Langevin model subjected to stochastic intensity noise (SIN), which incorporates temporal fluctuations in noise-intensity. We derive a higher-order Fokker-Planck equation (HFPE) of the system, taking into account the effect of SIN by the adiabatic elimination technique. Stationary distributions of the HFPE are calculated by using the perturbation expansion. We investigate the effect of SIN in three cases: (a) parabolic and quartic bistable potentials with additive noise, (b) a quartic potential with multiplicative noise, and (c) a stochastic gene expression model. We find that the existence of noise intensity fluctuations induces an intriguing phenomenon of a bimodal-to-trimodal transition in probability distributions. These results are validated with Monte Carlo simulations.

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