Stochastic Perturbations of Stable Dynamical Systems: Trajectory-Wise Approach

We study stochastic perturbations of a dynamical system with a locally stable fixed point. The perturbed system has the form of Ito stochastic differential equations. We assume that perturbations do not vanish at the equilibrium of the deterministic system. Using the approach based on consideration of trajectories to the analysis of stochastic differential equations, we find restrictions for perturbations under which the stability of the equilibrium is preserved with probability 1. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Authors
Publisher
Springer New York LLC
Number of issue
3
Language
English
Pages
340-353
Status
Published
Volume
241
Year
2019
Organizations
  • 1 Institute of Mathematics with Computer Center, Ufa Science Center of the Russian Academy of Sciences, Ufa, Russian Federation
  • 2 Peoples’ Friendship University of Russia, Moscow, Russian Federation
Keywords
34D10; 60H10; 93E15; dynamical system; perturbation; stability with probability 1; stochastic differential equation; white noise
Date of creation
24.12.2019
Date of change
24.12.2019
Short link
https://repository.rudn.ru/en/records/article/record/55024/