Geodesic
Van der Pol oscillator under random noise
Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 67-80

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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, moment functions, stochastic differential equation, random fluctuations, resonance, dispersive resonance.
Mots-clés : random perturbation 
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     title = {Van der {Pol} oscillator under random noise},
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E. V. Kuptsova. Van der Pol oscillator under random noise. Sibirskij žurnal industrialʹnoj matematiki, Tome 25 (2022) no. 3, pp. 67-80. http://geodesic.mathdoc.fr/item/SJIM_2022_25_3_a6/