Yu Qing, Liu Xianbin
State Key Laboratory of Mechanics and Control for Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, People's Republic of China.
Chaos. 2021 Sep;31(9):093110. doi: 10.1063/5.0056784.
Noise-induced escape in a 2D generalized Maier-Stein model with two parameters μ and α is investigated in the weak noise limit. With the WKB approximation, the patterns of extreme paths and singularities are displayed. By employing the Freidlin-Wentzell action functional and the asymptotic series, critical parameters α inducing singularity bifurcation are determined analytically for μ=1. The switching line will appear with singularities and is equivalent to the sliding set in the Filippov system. The pseudo-saddle-node bifurcation on the switching line is found. Then, when -1<μ<1, it is found that all bifurcation values α will decrease as μ decreases and the second-order bifurcation values are bigger than all first-order ones. In addition, the variation of the switching line is also analyzed and a new switching line will emerge when the location of the minimum quasi-potential on the boundary changes. At last, when the noise is anisotropic, only the noise intensity ratio will affect the bifurcation value α.
在弱噪声极限下，研究了具有两个参数μ和α的二维广义迈尔 - 斯坦模型中的噪声诱导逃逸。利用WKB近似，展示了极值路径和奇点的模式。通过使用弗雷德林 - 温策尔作用泛函和渐近级数，针对μ = 1解析地确定了引起奇点分岔的临界参数α。切换线将伴随着奇点出现，并且等同于菲利波夫系统中的滑动集。在切换线上发现了伪鞍结分岔。然后，当 -1 < μ < 1时，发现所有分岔值α将随着μ的减小而减小，并且二阶分岔值大于所有一阶分岔值。此外，还分析了切换线的变化，并且当边界上最小准势的位置发生变化时会出现一条新的切换线。最后，当噪声是各向异性时，只有噪声强度比会影响分岔值α。
