Normal forms approach to diffusion near hyperbolic equilibria
Normal forms approach to diffusion near hyperbolic equilibria
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DOI：
10.1088/0951-7715/24/6/011
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发表时间：
2010-06
期刊：
影响因子：
1.7
通讯作者：
Sergio A. Almada Monter;Yuri Bakhtin
中科院分区：
文献类型：
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作者：
Sergio A. Almada Monter;Yuri Bakhtin
考虑了双曲临界点附近平面上光滑动力系统小白色噪声扰动的出口问题。我们表明，如果分布的初始条件有一个缩放限制，然后退出分布和退出时间也有一个联合缩放限制的噪声强度为零。极限定律是明确计算的。这一结果完善了含噪异宿网络的二维理论。分析是基于范式理论。
We consider the exit problem for small white noise perturbation of a smooth dynamical system on the plane in the neighbourhood of a hyperbolic critical point. We show that if the distribution of the initial condition has a scaling limit then the exit distribution and exit time also have a joint scaling limit as the noise intensity goes to zero. The limiting law is computed explicitly. The result completes the theory of noisy heteroclinic networks in two dimensions. The analysis is based on normal forms theory.