Quasipotentials for coupled escape problems and the gate-height bifurcation.
Quasipotentials for coupled escape problems and the gate-height bifurcation.
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DOI：
10.1103/physreve.107.014213
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发表时间：
2022-09
期刊：
影响因子：
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通讯作者：
P. Ashwin;Jennifer L. Creaser;K. Tsaneva-Atanasova
中科院分区：
文献类型：
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作者：
P. Ashwin;Jennifer L. Creaser;K. Tsaneva-Atanasova
受噪声扰动的梯度动力系统的逃逸统计可以使用相关潜在景观的属性来估计。更一般地，Freidlin 和 Wentzell 准势 (QP) 可用于类似的目的，但计算它并不简单，而且它仅相对于某个起点进行定义。在本文中，我们重点计算耦合双稳态单元的准势，数值求解 Hamilton-Jacobi-Bellman 型问题。在耦合系统没有潜力的情况下，我们使用 QP 分析噪声引起的转换。门（吸引力盆地边界上相对于吸引子具有最小 QP 的点）用于了解盆地的逃逸率，但随着耦合强度的变化，这些门可能会发生全局变化。这种全局门高度分叉是小噪声参数化非梯度动力系统逃逸特性中的一般定性转变。
The escape statistics of a gradient dynamical system perturbed by noise can be estimated using properties of the associated potential landscape. More generally, the Freidlin and Wentzell quasipotential (QP) can be used for similar purposes, but computing this is nontrivial and it is only defined relative to some starting point. In this paper we focus on computing quasipotentials for coupled bistable units, numerically solving a Hamilton- Jacobi-Bellman type problem. We analyze noise induced transitions using the QP in cases where there is no potential for the coupled system. Gates (points on the boundary of basin of attraction that have minimal QP relative to that attractor) are used to understand the escape rates from the basin, but these gates can undergo a global change as coupling strength is changed. Such a global gate-height bifurcation is a generic qualitative transition in the escape properties of parametrized nongradient dynamical systems for small noise.