Stone Emily, Armbruster Dieter
Department of Mathematics and Statistics, Utah State University, Logan, Utah 84322-3900.
Chaos. 1999 Jun;9(2):499-506. doi: 10.1063/1.166423.
The dynamics of structurally stable heteroclinic cycles connecting fixed points with one-dimensional unstable manifolds under the influence of noise is analyzed. Fokker-Planck equations for the evolution of the probability distribution of trajectories near heteroclinic cycles are solved. The influence of the magnitude of the stable and unstable eigenvalues at the fixed points and of the amplitude of the added noise on the location and shape of the probability distribution is determined. As a consequence, the jumping of solution trajectories in and out of invariant subspaces of the deterministic system can be explained. (c) 1999 American Institute of Physics.
分析了在噪声影响下连接具有一维不稳定流形的不动点的结构稳定异宿环的动力学。求解了异宿环附近轨迹概率分布演化的福克 - 普朗克方程。确定了不动点处稳定和不稳定特征值的大小以及添加噪声的幅度对概率分布的位置和形状的影响。由此，可以解释解轨迹在确定性系统不变子空间内外的跳跃现象。（c）1999 美国物理学会。
