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Nonlinear dynamics of charged particle slipping on rough surface with periodic force

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Abstract

This paper deals with two types of period-doubling bifurcation phenomena in a particle system, where the charged particle slips on rough surface with periodic force. The charged particle system is characterized by a two-dimensional nonlinear mapping, i.e., the Fermi–Ulam model (FUM) with dissipation. Based on the dissipative FUM, theoretical investigations are performed to identify the two types of period-doubling bifurcations with the assist of eigenvalue analysis approach and further to reveal their underlying mechanisms of the particle system as the strength of the periodic force for the particle system increases. Finally, bifurcation diagram and the maximum Lyapunov exponent are employed to analyze the dynamical evolution of bifurcation behaviors in the particle system quantitatively. These results are helpful for the in-depth understanding of transport mechanism of charged particle system.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 51577141, 61571357) and Creative Foundation of the State Key Lab of Electrical Insulation and Power Equipment, China (Grant Nos. EIPE14308, EIPE 15309).

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Authors and Affiliations

  1. State Key Lab of Electrical Insulation and Power Equipment, School of Electrical Engineering, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Bo He, Huifang Ding, Hao Zhang & Yongpeng Meng

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  1. Bo He
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  2. Huifang Ding
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  3. Hao Zhang
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  4. Yongpeng Meng
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Correspondence to Hao Zhang.

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He, B., Ding, H., Zhang, H. et al. Nonlinear dynamics of charged particle slipping on rough surface with periodic force. Nonlinear Dyn 85, 2247–2259 (2016). https://doi.org/10.1007/s11071-016-2826-x

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