Noise-intensity fluctuation in Langevin model and its higher-order Fokker-Planck equation |
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Authors: | Yoshihiko Hasegawa Masanori Arita |
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Affiliation: | a Department of Biophysics and Biochemistry, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japanb Institute for Advanced Biosciences, Keio University, Yamagata 997-0035, Japan |
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Abstract: | 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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Keywords: | Stochastic process Superstatistics Stochastic volatility Adiabatic elimination Higher-order Fokker-Planck equation |
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