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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2007, Volume 47, Number 10, Pages 1692–1700
(Mi zvmmf230)
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Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation
T. V. Zavrazhina International Research and Educational Center for Information Technologies and Systems, National Academy of Sciences of Ukraine, pr. Akademika Glushkova 40, Kiev, 03680, Ukraine
Abstract:
A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in $\mathbb R^2$. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed.
Key words:
dynamical system, Duffing oscillator, periodic solution on a torus, bifurcation, chaos, Everhart numerical method,
Floquet theory, Feigenbaum universal constant.
Received: 12.07.2005 Revised: 10.05.2007
Citation:
T. V. Zavrazhina, “Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation”, Zh. Vychisl. Mat. Mat. Fiz., 47:10 (2007), 1692–1700; Comput. Math. Math. Phys., 47:10 (2007), 1622–1630
Linking options:
https://www.mathnet.ru/eng/zvmmf230 https://www.mathnet.ru/eng/zvmmf/v47/i10/p1692
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Abstract page: | 480 | Full-text PDF : | 151 | References: | 66 | First page: | 1 |
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