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Russia Yekaterinburg
Section Mathematics
Title The impact of colored noise on the equilibria of nonlinear dynamic systems
Author(-s) Bashkirtseva I.A.a
Affiliations Ural Federal Universitya
Abstract The influence of colored noise on the equilibrium regimes of nonlinear dynamical systems is investigated. To study the response of the system to small perturbations, we use an asymptotic approach that develops the stochastic sensitivity function technique. The stochastic sensitivity of equilibrium in a general multidimensional dynamical system is defined by some matrix. For this stochastic sensitivity matrix, we obtain a matrix algebraic equation. An exact solution of this equation is given for an important class of nonlinear oscillators with perturbations in the form of colored noises. This theory is applied to the parametric study of the response of the electronic generator with hard excitation to colored noises with various correlation times. The dependence of the dispersion of random states on the characteristic correlation time is investigated. It is shown that this dependence can be nonmonotonic and have maxima corresponding to the resonances. The paper discusses the probabilistic mechanism of the stochastic generation of large-amplitude oscillations caused by color noise.
Keywords colored noise, correlation time, stochastic sensitivity, electronic generator, stochastic excitability
UDC 519.21
MSC 93E03
DOI 10.20537/vm180201
Received 2 March 2018
Language Russian
Citation Bashkirtseva I.A. The impact of colored noise on the equilibria of nonlinear dynamic systems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 2, pp. 133-142.
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