ABSTRACT
We use the statistical modeling method to investigate the influence of the Wiener and Poisson random noise on the behavior of linear and Van der Pol oscillators. In the case of linear oscillator, an analytical expression of the autocovariance function of the solution to a stochastic differential equation (SDE) is obtained. This expression along with the formulas for the mathematical expectation and variance of the SDE solution allows us to carry out parametric analysis and investigate the accuracy of estimates for the moments of SDE numerical solution obtained based on the generalized explicit Euler method. In the case of the Van der Pol oscillator, the Poisson component influence on the nature of oscillations of the first and the second moments of the SDE solution at large jumps is investigated numerically.
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This work was carried out under the ICMMG SB RAS state assignment (project no. 0315-2019-0002).
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Yakunin, M.A. Parametric Analysis of Stochastic Oscillators by the Statistical Modeling Method. Numer. Analys. Appl. 13, 282–292 (2020). https://doi.org/10.1134/S1995423920030088
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DOI: https://doi.org/10.1134/S1995423920030088