Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems

Irina Bashkirtseva

doi:10.20944/preprints202406.0618.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 7 June 2024 / Approved: 10 June 2024 / Online: 11 June 2024 (10:57:08 CEST)

Motivated by important applications to the analysis of complex noise-induced phenomena, a problem of the constructive description of randomly forced equilibria for nonlinear systems with multiplicative noise is considered. Using apparatus of the first approximation systems, we construct an approximation of mean square deviations that explicitly takes into account the presence of multiplicative noise. This approximation is compared with the widely used approximation based on the stochastic sensitivity technique. The general mathematical results are illustrated with the example of the van der Pol oscillator with hard excitement.

Stochastic equilibria; multiplicative noise; second moments; approximations; dispersion

Computer Science and Mathematics, Probability and Statistics

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Approximations in Mean Square Analysis of Stochastically Forced Equilibria for Nonlinear Dynamical Systems

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