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A novel route to chaotic bursting in the parametrically driven Lorenz system

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Abstract

This paper aims to report a novel route to chaotic bursting, i.e., the route via bifurcation delay and chaos crisis, based on the parametrically driven Lorenz system. A distinct bifurcation delay behavior can be observed when the slowly varying parameter increases through pitchfork bifurcation point of the Lorenz system. The delay behavior may terminate at chaotic parameter areas, which leads to a catastrophic transition from the origin to the Lorenz strange attractor, and this accounts for the appearance of the chaotically active phase. On the other hand, the Lorenz strange attractor may collide with its attraction basin and suddenly disappears by boundary crisis and therein lies the occurrence of quiescence. Based on this, we propose the novel route to chaotic bursting and a new chaotic bursting pattern which we call “delayed pitchfork/boundary crisis” bursting is obtained.

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Acknowledgements

The authors express their gratitude to the associate editor and the reviewers whose comments and suggestions have helped the improvements in this paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 11572141, 11632008, 11472115, 11502091 and 11402226) and the Training Project for Young Backbone Teacher of Jiangsu University.

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Authors and Affiliations

  1. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, 212013, People’s Republic of China

    Xiujing Han

  2. School of Science, Nantong University, Nantong, 226007, People’s Republic of China

    Yue Yu

  3. School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, People’s Republic of China

    Chun Zhang

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  1. Xiujing Han
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Correspondence to Xiujing Han.

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Han, X., Yu, Y. & Zhang, C. A novel route to chaotic bursting in the parametrically driven Lorenz system. Nonlinear Dyn 88, 2889–2897 (2017). https://doi.org/10.1007/s11071-017-3418-0

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