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Complex Periodic Mixed-Mode Oscillation Patterns in a Filippov System

Author

Listed:
  • Chun Zhang

    (School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China)

  • Qiaoxia Tang

    (School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China)

Abstract

The main task of this article is to study the patterns of mixed-mode oscillations and non-smooth behaviors in a Filippov system with external excitation. Different types of periodic spiral crossing mixed-mode oscillation patterns, i.e., “cusp-F − /fold-F − ” oscillation, “cusp-F − /two-fold/two-fold/fold-F − ” oscillation and “two-fold/fold-F − ” oscillation, are explored. Based on the analysis of the equilibrium and tangential singularities of the fast subsystem, spiral crossing oscillation around the tangential singularities is investigated. Meanwhile, by combining the fast and slow analysis methods, we can observe that the cusp, two-fold and fold-cusp singularities play an important role in generating all kinds of complex mixed-mode oscillations.

Suggested Citation

  • Chun Zhang & Qiaoxia Tang, 2022. "Complex Periodic Mixed-Mode Oscillation Patterns in a Filippov System," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:673-:d:755299
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    References listed on IDEAS

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    1. Santolo Meo & Luisa Toscano, 2021. "On the Existence and Uniqueness of the ODE Solution and Its Approximation Using the Means Averaging Approach for the Class of Power Electronic Converters," Mathematics, MDPI, vol. 9(10), pages 1-12, May.
    2. Ma, Xindong & Yu, Yue & Wang, Lifeng, 2021. "Complex mixed-mode vibration types triggered by the pitchfork bifurcation delay in a driven van der Pol-Duffing oscillator," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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