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Stationary distribution simulation of rare events under colored Gaussian noise

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Abstract

Forward flux sampling (FFS) has provided a convenient and efficient way to simulate rare events in equilibrium as well as non-equilibrium stochastic systems. In the present paper, the FFS scheme is applied to systems driven by colored Gaussian noise through enlarging the dimension to deal with the non-Markovian property. Besides, the parameters of the FFS scheme have to be reconsidered. Interestingly, by analyzing the effect of colored Gaussian noise on stationary distributions, some results are found which are clearly different from the case of Gaussian white noise excitation. We mainly found that the probability of the occurrence of rare events is inversely proportional to the correlation time. Comparing to the case of Gaussian white noise with the same intensity, the presence of colored Gaussian noise exerts a hindrance to the occurrence of rare events. Meanwhile, the FFS results show a good agreement with those from Monte Carlo simulations, even for the colored Gaussian noise case. This provides a potential insight into rare events of systems under non-white Gaussian noise via the FFS scheme.

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, P.R. China

    Hua Li, Yong Xu & Xiaole Yue

  2. MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710072, P.R. China

    Yong Xu

  3. Department of Physics, Humboldt University of Berlin, Berlin, 12489, Germany

    Yong Xu & Jürgen Kurths

  4. Potsdam Institute for Climate Impact Research, Potsdam, 14412, Germany

    Yong Xu & Jürgen Kurths

Authors
  1. Hua Li
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  2. Yong Xu
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  3. Jürgen Kurths
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  4. Xiaole Yue
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Correspondence to Yong Xu.

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Li, H., Xu, Y., Kurths, J. et al. Stationary distribution simulation of rare events under colored Gaussian noise. Eur. Phys. J. B 92, 76 (2019). https://doi.org/10.1140/epjb/e2019-100022-y

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  • DOI: https://doi.org/10.1140/epjb/e2019-100022-y

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