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Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation

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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 ℝ2. 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.

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Authors and Affiliations

  1. International Research and Educational Center for Information Technologies and Systems, National Academy of Sciences of Ukraine, pr. Akademika Glushkova 40, Kiev, 03680, Ukraine

    T. V. Zavrazhina

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  1. T. V. Zavrazhina
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Correspondence to T. V. Zavrazhina.

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Original Russian Text © T.V. Zavrazhina, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 10, pp. 1692–1700.

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Zavrazhina, T.V. Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation. Comput. Math. and Math. Phys. 47, 1622–1630 (2007). https://doi.org/10.1134/S0965542507100041

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  • DOI: https://doi.org/10.1134/S0965542507100041

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