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Non-Smooth Dynamic Behaviors as well as the Generation Mechanisms in a Modified Filippov-Type Chua’s Circuit with a Low-Frequency External Excitation

Author

Listed:
  • Hongfang Han

    (Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
    School of Mechanical Engineering and Rail Transit, Changzhou University, Changzhou 213016, China)

  • Shaolong Li

    (Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China)

  • Qinsheng Bi

    (Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China)

Abstract

The main purpose of this paper is to study point-cycle type bistability as well as induced periodic bursting oscillations by taking a modified Filippov-type Chua’s circuit system with a low-frequency external excitation as an example. Two different kinds of bistable structures in the fast subsystem are obtained via conventional bifurcation analyses; meanwhile, nonconventional bifurcations are also employed to explain the nonsmooth structures in the bistability. In the following numerical investigations, dynamic evolutions of the full system are presented by regarding the excitation amplitude and frequency as analysis parameters. As a consequence, we can find that the classification method for periodic bursting oscillations in smooth systems is not completely applicable when nonconventional bifurcations such as the sliding bifurcations and persistence bifurcation are involved; in addition, it should be pointed out that the emergence of the bursting oscillation does not completely depend on bifurcations under the point-cycle bistable structure in this paper. It is predicted that there may be other unrevealed slow–fast transition mechanisms worthy of further study.

Suggested Citation

  • Hongfang Han & Shaolong Li & Qinsheng Bi, 2022. "Non-Smooth Dynamic Behaviors as well as the Generation Mechanisms in a Modified Filippov-Type Chua’s Circuit with a Low-Frequency External Excitation," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3613-:d:932332
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