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      https://www.ias.ac.in/article/fulltext/pram/094/0014

    • Keywords

       

      Filippov-type system; mixed-mode oscillations; bifurcation; transformed phase portrait

    • Abstract

       

      In this paper, mixed-mode oscillations and bifurcation mechanism for a Filippov-type system including two time-scales in the frequency domain are demonstrated. According to classic Chua’s system, we investigate a non-smooth dynamical system including two time-scales. As there exists an order gap between the exciting frequency and the natural one, the whole external excitation term can be considered as a slow-changing parameter, which results in two smooth subsystems divided by the non-smooth boundary. In addition, the critical condition about fold bifurcation (FB) is studied, and by applying the Hopf bifurcation (HB) theorem, specific formulas for determining the existence of HBs are presented. By introducing an auxiliary parameter via differential inclusions theory, the non-smoothbifurcations on the boundary are discussed. Then, the equilibrium branches and the bifurcations are derived, and two typical cases associated with different bifurcations are considered. In light of the superposition between the bifurcation curve and the transformed phase portrait, the dynamical behaviours of the mixed-mode oscillations as well as sliding movement along the non-smooth boundary are obtained, which reveal the corresponding dynamical mechanism.

    • Author Affiliations

       

      MIAO PENG1 ZHENGDI ZHANG1 ZIFANG QU1 QINSHENG BI2

      1. Faculty of Science, Jiangsu University, Zhenjiang 212013, China
      2. Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013, China
    • Dates

       
  • Pramana – Journal of Physics | News

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      Posted on July 25, 2019

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