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On two-parameter bifurcation analysis of the periodic parameter-switching Lorenz oscillator

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Abstract

By introducing the periodic parameter-switching scheme to the Lorenz oscillator, a switched dynamic model is established. In order to investigate the mechanism of the behaviors of the switched system, the Poincaré map of the whole system is defined by suitable local sections and local maps. Different types of periodic oscillations and their transitions to chaos in the system can be observed. Based on the conditions when the Floquet multiplies of corresponding fixed point associated with the periodic solution pass the unit circle, some bifurcation curves are obtained in the plane of bifurcation parameters, dividing the parameters plane into several regions corresponding to different kinds of oscillations. Meanwhile, bifurcation scenarios, such as fold bifurcation, pitchfork bifurcation and period-doubling bifurcation, are determined in the switched system.

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Acknowledgments

The authors thank the anonymous reviewers for their valuable comments and suggestions that help to improve the presentation of the paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 21276115, 11272135 and 11202085), the Natural Science Foundation for Colleges and Universities of Jiangsu Province (Grant No. 11KJB130001) and the Research Foundation for Advanced Talents of Jiangsu University (Grant Nos. 11JDG065 and 11JDG075).

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Authors and Affiliations

  1. School of Mathematical Science, Huaiyin Normal University, Huai’an, 223300, Jiangsu, People’s Republic of China

    Chun Zhang

  2. Faculty of Science, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Qinsheng Bi

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

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Zhang, C., Bi, Q. On two-parameter bifurcation analysis of the periodic parameter-switching Lorenz oscillator. Nonlinear Dyn 81, 577–583 (2015). https://doi.org/10.1007/s11071-015-2012-6

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  • DOI: https://doi.org/10.1007/s11071-015-2012-6

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