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Bifurcation and number of subharmonic solutions of a 2n-dimensional non-autonomous system and its application

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Abstract

This paper is devoted to consider the existence and bifurcation of subharmonic solutions of two types of 2n-dimensional nonlinear systems with time-dependent perturbations. When the unperturbed system is a Hamiltonian system, we obtain the extended Melnikov function by means of performing the curvilinear coordinate frame and constructing a Poincaré map. Then some conditions of the bifurcation of subharmonic solutions are obtained. The results obtained in this paper contain and improve the existing results for \(n=2,3\). When the unperturbed system contains an isolated invariant torus, we investigate the bifurcation of subharmonic solutions by analyzing the Poincaré map. We apply the extended Melnikov method to study the bifurcation and number of subharmonic solutions of the ice-covered suspension system. The maximum number of subharmonic solutions of this system is 2, and the relative parameter control condition is obtained.

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Acknowledgements

The research project is supported by National Natural Science Foundation of China (11802200, 11772007, 11372014, 11832002, 11290152) and also supported by Beijing Natural Science Foundation (1172002, Z180005) and the International Science and Technology Cooperation Program of China (2014DFR61080).

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Authors and Affiliations

  1. School of Science, Tianjin Chengjian University, Tianjin, 300384, People’s Republic of China

    Tingting Quan & Min Sun

  2. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Tingting Quan & Jing Li

  3. College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Wei Zhang

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  1. Tingting Quan
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  2. Jing Li
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  3. Wei Zhang
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  4. Min Sun
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Correspondence to Jing Li.

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Quan, T., Li, J., Zhang, W. et al. Bifurcation and number of subharmonic solutions of a 2n-dimensional non-autonomous system and its application. Nonlinear Dyn 98, 301–315 (2019). https://doi.org/10.1007/s11071-019-05192-2

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  • DOI: https://doi.org/10.1007/s11071-019-05192-2

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