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Qu Zifang, Zhang Zhengdi, Peng Miao, Bi Qinsheng. NON-SMOOTH BURSTING OSCILLATION MECHANISMS IN A FILIPPOV-TYPE SYSTEM WITH MULTIPLE PERIODIC EXCITATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1145-1155. DOI: 10.6052/0459-1879-18-136
Citation: Qu Zifang, Zhang Zhengdi, Peng Miao, Bi Qinsheng. NON-SMOOTH BURSTING OSCILLATION MECHANISMS IN A FILIPPOV-TYPE SYSTEM WITH MULTIPLE PERIODIC EXCITATIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018, 50(5): 1145-1155. DOI: 10.6052/0459-1879-18-136
shu

NON-SMOOTH BURSTING OSCILLATION MECHANISMS IN A FILIPPOV-TYPE SYSTEM WITH MULTIPLE PERIODIC EXCITATIONS

  • *(Faculty of Science, Jiangsu University, Zhenjiang 212013, Jiangsu, China)

  • †(School of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005, Shandong, China)

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

  • Received Date: April 24, 2018
    Graphical Abstract
    • Abstract
  • The main purpose of this paper is to explore non-smooth bursting oscillations as well as the bifurcation mechanisms in a Filippov-type system with different scales and two periodic excitations. By using the coupling of Duffing and Van der Pol oscillators as the dynamical system model and introducing two periodically changed electrical sources, the two periodic excitations can be converted into a function of a single periodic exciting term which can be considered as a slow-varying parameter when there is an order gap between the exciting frequency and the natural one. The equilibrium branches as well as the bifurcation mechanisms which are caused by fold or Hopf bifurcations with the variation of the slow-varying parameter are obtained in the case of two different frequencies of parametric excitation when the amplitudes of two periodic excitations are constants. Based on the transformed phase portraits and the evolutions of stable limit cycles produced by Hopf bifurcations, the critical conditions of multisliding bifurcations and various oscillation modes determined by a slow-varying parameter are derived. The oscillation mechanisms and the analysis of the non-smooth dynamic behaviors are also described in detail. By contrasting the equilibrium branches with two different frequencies of the parametric excitation, we find the equilibrium branches become more tortuous although the equilibrium branches are similar in the structure. The number of the corresponding extreme points are also changed, and the results are verified by numerical simulations.
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