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Complex period-1 motions of a periodically forced Duffing oscillator with a time-delay feedback

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An Erratum to this article was published on 25 June 2014

Abstract

In this paper, complex period-1 motions in a periodically forced Duffing oscillator with a time-delay feedback are investigated, and the symmetric and asymmetric, complex period-1 motions exist in lower excitation frequency. The analytical solutions of complex period-1 motions in such a Duffing oscillator are obtained through the finite Fourier series, and the corresponding stability and bifurcations of complex period-1 motions are discussed by eigenvalue analysis. The frequency–amplitude characteristics of complex period-1 motions in the periodically forced Duffing oscillator with a time-delay feedback are discussed. Complex period-1 motions generated numerically and analytically are illustrated. As excitation frequency is close to zero, the complex period-1 motions need almost infinite harmonic terms in the Fourier series to express the analytical solutions. From this study, the initial time-delay in the time-delayed, nonlinear systems should be uniquely determined to achieve a specific periodic motion.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Southern Illinois University Edwardsville, Edwardsville, IL, 62026-1805, USA

    Albert C. J. Luo & Hanxiang Jin

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  1. Albert C. J. Luo
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  2. Hanxiang Jin
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Correspondence to Albert C. J. Luo.

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Luo, A.C.J., Jin, H. Complex period-1 motions of a periodically forced Duffing oscillator with a time-delay feedback. Int. J. Dynam. Control 3, 325–340 (2015). https://doi.org/10.1007/s40435-014-0091-8

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  • DOI: https://doi.org/10.1007/s40435-014-0091-8

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