Transition-event duration in one-dimensional systems under correlated noise
Transition-event duration in one-dimensional systems under correlated noise
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相关噪声下一维系统中的过渡事件持续时间
DOI：
10.1016/j.physa.2019.121764
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发表时间：
2019-10
期刊：
影响因子：
--
通讯作者：
Kurths Juergen
中科院分区：
文献类型：
--
作者：
Li Hua;Xu Yong;Yue Xiaole;Kurths Juergen
跃迁事件持续时间(TED)是粒子进入一种状态的邻域到达另一种状态而不再返回到其开始的状态所花费的时间。本文提出了一种近似理论方法来获得相关噪声下一维双稳态强非线性系统的跃迁事件持续时间分布(TEDD)。它有力地扩展了现有的获得TEDD的理论方法。实际上，TEDD的近似理论解是由带有两个吸收边界条件的Fokker-Planck方程(FPE)确定的。在这里，我们将每个吸收边界条件设置在双稳态势函数的稳定点和不稳定点。首先，用C型Gram-Charlier展开法给出了一种求解FPE的方法。随后，基于加权残差方法，将FPE化为一系列系数未知的常微分方程组。然后，通过求解这一系列的常微分方程组，得到了TEDD的解析解。特别地，系统的随机激励可以分为五种情况：高斯白噪声、有色高斯噪声、两个白互相关高斯白噪声、两个指数相关高斯白噪声和两个指数相关有色高斯噪声。我们主要讨论了相关系数和噪声参数对TEDD的影响。将相应的解析结果与蒙特卡罗模拟结果进行了比较，得到了较好的一致性。
Transition-event duration (TED) is the spent time of a particle which enters a neighborhood of one state to reach another one without ever returning back to the state where it starts. In this paper, an approximate theoretical method is proposed to obtain the transition-event duration distribution (TEDD) of one-dimensional bi-stable strongly nonlinear systems under correlated noises. It strongly extends the existing theoretical methods for obtaining the TEDD. Actually, an approximate theoretical solution of the TEDD is determined by the Fokker–Planck equation (FPE) with two absorbing boundary conditions. Here, we set each absorbing boundary condition at stable and unstable points of a bi-stable potential function. Firstly, a solution to the FPE is presented by the C-type Gram–Charlier expansion. Subsequently, based on the weighted residual scheme, the FPE is reduced to a series of ordinary differential equations (ODEs) with unknown coefficient. Then, an analytical solution to TEDD is derived by solving this series of ODEs. Especially, the concerning stochastic excitations of the system can be divided into five kinds of situations: Gaussian white noise, colored Gaussian noise, two Gaussian white noises with white cross-correlation, two Gaussian white noises with exponential correlation and two colored Gaussian noises with exponential correlation. We mainly discuss the influences of correlation and the parameters of noise on the TEDD. Our corresponding analytic results are compared with Monte Carlo simulations, and good agreements are found.
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影响因子：
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