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Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance

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Abstract

An oscillator with dry friction under external excitation is considered. The Poincaré map can be established according to the series solution near equilibrium in the case of 1:4 resonance. Based on the theory of normal forms, the map is reduced into its normal form. It is shown that the Neimark-Sacker (N-S) bifurcations may occour. The theoretical results are verified with the numerical simulations.

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Authors and Affiliations

  1. School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 610031, P. R. China

    Yong Guo  (郭 勇) & Jian-hua Xie  (谢建华)

Authors
  1. Yong Guo  (郭 勇)
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  2. Jian-hua Xie  (谢建华)
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Corresponding author

Correspondence to Jian-hua Xie  (谢建华).

Additional information

Communicated by Li-qun CHEN

Project supported by the National Natural Science Foundation of China (No. 11172246) and the Fundamental Research Funds for the Central Universities of China (No.SWJTU11ZT15)

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Guo, Y., Xie, Jh. Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance. Appl. Math. Mech.-Engl. Ed. 34, 27–36 (2013). https://doi.org/10.1007/s10483-013-1650-9

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  • DOI: https://doi.org/10.1007/s10483-013-1650-9

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2010 Mathematics Subject Classification

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