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Dynamical behaviors of the periodic parameter-switching system

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Abstract

In this paper, a periodic parameter-switching system about Lorenz oscillators is established. To investigate the bifurcation behavior of this system, Poincaré mapping of the whole system is defined by suitable local sections and local mappings. The location of the fixed point and the parameter values of local bifurcations are calculated by the shooting method and Runge–Kutta method. Then based on the Floquent theory, we conclude that the period-doubling and saddle-node bifurcations play an important role in the generation of various periodic solutions and chaos. Meanwhile, upon the analysis of the equilibrium points of the subsystems, we explore the mechanisms of different periodic switching oscillations.

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Acknowledgements

The authors thank the anonymous reviewers for their valuable comments and suggestions that helped to improve the presentation of the paper. This work is supported by the Natural Science Foundation of China (Grant Nos. 21276115 and 11202085) and the Research Foundation for Advanced Talents of Jiangsu University (Grant Nos. 11JDG065 and 11JDG075).

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  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, China

    Chun Zhang, Xiujing Han & Qinsheng Bi

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  1. Chun Zhang
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  2. Xiujing Han
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Correspondence to Qinsheng Bi.

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Zhang, C., Han, X. & Bi, Q. Dynamical behaviors of the periodic parameter-switching system. Nonlinear Dyn 73, 29–37 (2013). https://doi.org/10.1007/s11071-013-0764-4

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