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Bursting oscillations with boundary homoclinic bifurcations in a Filippov-type Chua’s circuit

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Abstract

A modified version of the typical Chua’s circuit, which possesses a periodic external excitation and a piecewise nonlinear resistor, is considered to investigate the possible bursting oscillations and the dynamical mechanism in the Filippov system. Two new symmetric periodic bursting oscillations are observed when the frequency of external excitation is far less than the natural one. Besides the conventional Hopf bifurcation, two non-smooth bifurcations, i.e., boundary homoclinic bifurcation and non-smooth fold limit cycle bifurcation, are discussed when the whole excitation term is regarded as a bifurcation parameter. The sliding solution of the Filippov system and pseudo-equilibrium bifurcation of the sliding vector field on the switching manifold are analysed theoretically. Based on the analysis of the bifurcations and the sliding solution, the dynamical mechanism of the bursting oscillations is revealed. The external excitation plays an important role in generating bursting oscillations. That is, bursting oscillations may be formed only if the excitation term passes through the boundary homoclinic bifurcation. Otherwise, they do not occur. In addition, the time intervals between two symmetric adjacent spikes of the bursting oscillations and the duration of the system staying at the stable pseudonode are dependent on the excitation frequency.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos 11632008, 11872189).

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Authors and Affiliations

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

    Zhixiang Wang & Qinsheng Bi

  2. School of Mathematics and Statistics, Huaiyin Normal University, Huai’an, 223300, China

    Zhixiang Wang & Chun Zhang

  3. Faculty of Science, Jiangsu University, Zhenjiang, 212013, China

    Zhengdi Zhang

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  1. Zhixiang Wang
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  2. Chun Zhang
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  4. Qinsheng Bi
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Correspondence to Qinsheng Bi.

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Wang, Z., Zhang, C., Zhang, Z. et al. Bursting oscillations with boundary homoclinic bifurcations in a Filippov-type Chua’s circuit. Pramana - J Phys 94, 95 (2020). https://doi.org/10.1007/s12043-020-01976-z

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  • DOI: https://doi.org/10.1007/s12043-020-01976-z

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