论文标题
耦合逃生问题和闸门高叉式分叉的准次电位
Quasipotentials for coupled escape problems and the gate-height bifurcation
论文作者
论文摘要
可以使用相关潜在景观的性质估算噪声扰动的梯度动力学系统的逃生统计数据。更一般而言，Freidlin和Wentzell准能力（QP）可用于类似目的，但是计算这是非平凡的，并且仅相对于某个起点而定义。在本文中，我们专注于计算耦合双单元的准次电位，以数字解决汉密尔顿 - 雅各比 - 贝尔曼类型问题。在没有耦合系统潜力的情况下，我们使用QP分析了噪声诱导的过渡。大门（相对于吸引人的吸引盆地边界的点，相对于该吸引子的质量最小）用于了解盆地的逃生速率，但是随着耦合强度的改变，这些大门可以发生全球变化。这样的全局栅极高分子是用于小噪声的参数性非梯度动力学系统的逃生特性中的通用定性过渡。
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 non-trivial 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 analyse 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 transitions in the escape properties of parametrised non-gradient dynamical systems for small noise.
