Levy noise-induced escape in an excitable system
Levy noise-induced escape in an excitable system
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可兴奋系统中的 Levy 噪声引起的逃逸
DOI：
10.1088/1742-5468/aa727c
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发表时间：
2017
影响因子：
2.4
通讯作者：
Li Xiaofan
中科院分区：
文献类型：
--
作者：
Cai Rui;Chen Xiaoli;Duan Jinqiao;Kurths Juergen;Li Xiaofan
本文研究了对称α-稳定lsamvy噪声驱动下的随机FitzHugh-Nagumo （FHN）神经元模型的逃逸动力学。外部或内部刺激可能使可兴奋系统产生脉冲或不产生脉冲，这可以解释为逃逸问题。提出了一种分析静态到激发态状态转换的新方法。该方法由两个确定性指标组成：首次逃逸概率（FEP）和平均首次逃逸时间（MFET）。我们发现静止态（平衡态）较高的FEP促进了这种转变，而MFET直接反映了静止态的稳定性与所选择的逸出区。所建立的二维数值模拟方法不仅可以避免FEP和MFET的降维，而且适用于噪声较大的情况。此外，FEP为我们理解随机FHN模型的分离矩阵提供了一个新的视角。可以看出，较小的lsamvy运动跳跃和相对较小的噪声强度有利于峰值的产生。为了表征噪声对所选逸出区域的影响，计算了逸出区域中较高FEP和MFET的面积。同时，也考虑了布朗运动作为一种特殊情况进行比较。
This paper considers the dynamics of escape in the stochastic FitzHugh–Nagumo (FHN) neuronal model driven by symmetric α-stable Lévy noise. External or internal stimulation may make the excitable system produce a pulse or not, which can be interpreted as an escape problem. A new method to analyse the state transition from the rest state to the excitatory state is presented. This approach consists of two deterministic indices: the first escape probability (FEP) and the mean first exit time (MFET). We find that higher FEP in the rest state (equilibrium) promotes such a transition and MFET reflects the stability of the rest state directly with the selected escape region. The developed two dimensional numerical simulation method to calculate FEP and MFET can not only avoid a dimension reduction, but is also applicable for the cases with large noise. In addition, FEP provides us with a new perspective to understand the seperatrix of the stochastic FHN model. It can be seen that smaller jumps of the Lévy motion and relatively small noise intensity are conducive to the production of spikes. In order to characterize the effect of noise on the selected escape region in which the equilibrium lies, the area of higher FEP and MFET in the escape region are calculated. Meanwhile, Brownian motion as a special case is also taken into account for comparison.