Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 675–694
This article is cited in 2 scientific papers (total in 2 papers)
Asymptotic and numerical analysis of parametric resonance in a nonlinear system of two oscillators
N. A. Lyulkoab, N. A. Kudryavtsevab, A. N. Kudryavtsevcb
a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
c Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
A parametric resonance in a nonlinear system of ordinary differential equations, which is a mathemetical model of a water–oil gas containing layer, is considered. The Krylov–Bolgoliubov–Mitropolsky averaging method is applied to investigate the instability of zero solution of the system and deduce averaged equations for time evolution of the amplitude of oscillations in the cases of main and combinational resonances. The original and averaged equations are also integrated numerically with a high-order strong stability preserving Runge–Kutta scheme. By comparing the numerical solutions it is shown that the averaged equations enable us to predict correctly the maximum amplitude of oscillations and the time moment when it is achieved. The dependence of resonance characteritics on the small parameter is also studied.
instability in nonlinear system of two oscillators, main and combinational parametric resonances, asymptotic and numerical analysis of resonance.
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Received April 21, 2014, published August 30, 2014
N. A. Lyulko, N. A. Kudryavtseva, A. N. Kudryavtsev, “Asymptotic and numerical analysis of parametric resonance in a nonlinear system of two oscillators”, Sib. Èlektron. Mat. Izv., 11 (2014), 675–694
Citation in format AMSBIB
\by N.~A.~Lyulko, N.~A.~Kudryavtseva, A.~N.~Kudryavtsev
\paper Asymptotic and numerical analysis of parametric resonance in a nonlinear system of two oscillators
\jour Sib. \`Elektron. Mat. Izv.
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N. A. Lyul'ko, “Instability of a nonlinear system of two oscillators under main and combination resonances”, Comput. Math. Math. Phys., 55:1 (2015), 53–70
V. S. Belonosov, “Asymptotic analysis of the parametric instability of nonlinear hyperbolic equations”, Sb. Math., 208:8 (2017), 1088–1112
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