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Dynamics and delayed feedback control for a 3D jerk system with hidden attractor

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Abstract

A 3D jerk system with only one stable equilibria was presented and discussed. Some periodic orbits and chaotic behaviors of this system are obtained. Meanwhile, a delayed feedback control scheme for this system was proposed. By using the method of projection for center manifold computation, Hopf bifurcation for the delayed feedback control system was analyzed and obtained. The simulation results demonstrate the correctness of the Hopf bifurcation analysis and the effectiveness of the proposed delayed feedback control strategy.

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Acknowledgments

The author acknowledges the referees and the editor for carefully reading this paper and suggesting many helpful comments. This work was supported by the Natural Science Foundation of China (No. 61473237, 11401543), the China Postdoctoral Science Foundation funded project (No. 2014M560028), the Natural Science Foundation of Hubei Province (No. 2014CFB897), the Visting Scholar Foundation of Key Lab and the Scientific Research Foundation of Xijing University (Grant No. XJ130245, XJ13ZD02, XJ13B03).

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Authors and Affiliations

  1. Department of Applied Statistics and Science, Xijing University, Xi’an, 710123, People’s Republic of China

    Zhen Wang, Wei Sun & Shanwen Zhang

  2. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, People’s Republic of China

    Zhouchao Wei

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  1. Zhen Wang
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  2. Wei Sun
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Correspondence to Zhen Wang.

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Wang, Z., Sun, W., Wei, Z. et al. Dynamics and delayed feedback control for a 3D jerk system with hidden attractor. Nonlinear Dyn 82, 577–588 (2015). https://doi.org/10.1007/s11071-015-2177-z

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