Yukalov V I
Research Center for Optics and Photonics, Instituto de Fisica de São Carlos, Universidade de São Paulo, Caixa Postal 369, São Carlos, São Paulo 13560-970, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 May;65(5 Pt 2):056118. doi: 10.1103/PhysRevE.65.056118. Epub 2002 May 17.
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with respect to infinite time describes the asymptotic stability of a stochastic dynamical system. Another limit of the stability index is given by the vanishing intensity of stochastic perturbations. A dynamical system is stochastically unstable when these two limits do not commute with each other. Several examples illustrate the thesis that there always exist such stochastic perturbations that render a given dynamical system stochastically unstable. The stochastic instability of quasi-isolated systems is responsible for the irreversibility of time arrow.
考虑了具有小随机扰动的演化方程解的稳定性。随机动力系统的稳定性由局部稳定性指标来表征。该指标关于无限时间的极限描述了随机动力系统的渐近稳定性。稳定性指标的另一个极限由随机扰动强度的消失给出。当这两个极限不相互交换时，动力系统是随机不稳定的。几个例子说明了这样一个论点，即总是存在使给定动力系统随机不稳定的随机扰动。准孤立系统的随机不稳定性是时间箭头不可逆性的原因。
