Levy noise-induced escape in an excitable system

被引:31
作者
Cai, Rui [1 ,2 ]
Chen, Xiaoli [1 ,2 ]
Duan, Jinqiao [3 ]
Kurths, Juergen [4 ,5 ]
Li, Xiaofan [3 ]
机构
[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China
[2] Huazhong Univ Sci & Technol, Ctr Math Sci, Wuhan 430074, Peoples R China
[3] IIT, Dept Appl Math, Chicago, IL 60616 USA
[4] Potsdam Inst Climate Impact Res, Res Domain Transdisciplinary Concepts & Methods, POB 60 12 03, D-14412 Potsdam, Germany
[5] Humboldt Univ, Dept Phys, Newtonstr 15, D-12489 Berlin, Germany
基金
美国国家科学基金会;
关键词
Noise models; Neuromorphic models; Nonlinear dynamics and Brownian motion; INDUCED STOCHASTIC RESONANCE; COHERENCE RESONANCE; STABILIZATION; TRANSITIONS; DRIVEN; STATE;
D O I
10.1088/1742-5468/aa727c
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
This paper considers the dynamics of escape in the stochastic FitzHugh-Nagumo (FHN) neuronal model driven by symmetric alpha-stable Levy 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 Levy 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.
引用
收藏
页数:19
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