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Periodic bursting oscillations involving stick–slip motions as well as the generation mechanism in a Filippov-type slow–fast dynamical system

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Abstract

By taking a low-frequency excited modified Chua’s circuit model with discontinuous vector field as an academic example, this paper introduces the periodic bursting patterns characterised by stick–slip motions as well as the underlying generation mechanism uniquely belonging to Filippov-type slow–fast dynamical systems (FSFDSs). Based on the tangencies and the visibilities, this paper is the first to clearly explain the unique transition routes to bursting phenomena involving stick–slip motions by introducing the subdivisions of the sliding region. The results indicate that such transition routes are heavily dependent on the local structures of pseudoequilibrium (PE), performing distinct non-conventional bifurcation schemes. Furthermore, two transition routes respectively corresponding to a stable node-type PE and a stable focus-type PE as well as the induced periodic bursting oscillations are further discussed in numerical simulations. Particularly, it should be pointed out that the second one is a novel route to bursting oscillation in FSFDSs.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos 11632008, 1200-2299 and 11872189) and the Scientific Research Innovation Foundation of Jiangsu Province (Grant No. KYLX15_1044).

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Authors and Affiliations

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

    Shaolong Li, Hongfang Han, Rui Qu, Weipeng Lv & Qinsheng Bi

  2. Faculty of Mathematics and Statistics, Yancheng Teachers University, Yancheng, 224005, China

    Shaolong Li & Weipeng Lv

Authors
  1. Shaolong Li
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  2. Hongfang Han
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  3. Rui Qu
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  4. Weipeng Lv
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  5. Qinsheng Bi
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Correspondence to Shaolong Li.

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Li, S., Han, H., Qu, R. et al. Periodic bursting oscillations involving stick–slip motions as well as the generation mechanism in a Filippov-type slow–fast dynamical system. Pramana - J Phys 97, 22 (2023). https://doi.org/10.1007/s12043-022-02500-1

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  • DOI: https://doi.org/10.1007/s12043-022-02500-1

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