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DOE OSTI · 22921152

Stochastic Perturbations of Stable Dynamical Systems: Trajectory-Wise Approach

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Abstract

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.

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97 MATHEMATICS AND COMPUTINGDIFFERENTIAL EQUATIONSDISTURBANCESDYNAMICAL SYSTEMSEQUILIBRIUMNOISEPERTURBATION THEORYPROBABILITYSTABILITYSTOCHASTIC PROCESSES

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2019-09-07. Stochastic Perturbations of Stable Dynamical Systems: Trajectory-Wise Approach. https://doi.org/10.1007/s10958-019-04428-1

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