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Van der Pol oscillator under random noise
E. V. Kuptsova Krasovskii Institute of Mathematics and Mechanics UB RAS, ul. S. Kovalevskaya 16, Yekaterinburg 620108, Russia
Abstract:
It is believed that the perturbations are of random nature. For a mathematical model of an oscillator, the first approximations for the mathematical expectation and the dispersion function of the solution are found in the form of a differential equation with a small parameter perturbed by random noise. It is assumed that the disturbances are random and it is not assumed that they are generated by white noise. The conditions for the resonance of the mathematical expectation of the solution for the harmonic average value of the disturbing random noise are obtained. A new fact has been established: the increase of the dispersion function with increasing time (dispersion resonance), if five algebraic equalities for the moment functions of a random perturbation are not fulfilled.
Keywords:
electric oscillator, random perturbation, moment functions, stochastic differential equation, random fluctuations, resonance, dispersive resonance.
Received: 01.06.2020 Revised: 22.01.2022 Accepted: 22.06.2022
Citation:
E. V. Kuptsova, “Van der Pol oscillator under random noise”, Sib. Zh. Ind. Mat., 25:3 (2022), 67–80
Linking options:
https://www.mathnet.ru/eng/sjim1183 https://www.mathnet.ru/eng/sjim/v25/i3/p67
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