QIN Zhao-hong, CHEN Yu-shu. Singularity Analysis of Duffing-van der Pol System With Two Bifurcation Parameters Under Multi-Frequency Excitations[J]. Applied Mathematics and Mechanics, 2010, 31(8): 971-978. doi: 10.3879/j.issn.1000-0887.2010.08.009
Citation: QIN Zhao-hong, CHEN Yu-shu. Singularity Analysis of Duffing-van der Pol System With Two Bifurcation Parameters Under Multi-Frequency Excitations[J]. Applied Mathematics and Mechanics, 2010, 31(8): 971-978. doi: 10.3879/j.issn.1000-0887.2010.08.009

Singularity Analysis of Duffing-van der Pol System With Two Bifurcation Parameters Under Multi-Frequency Excitations

doi: 10.3879/j.issn.1000-0887.2010.08.009
  • Received Date: 1900-01-01
  • Rev Recd Date: 2010-05-29
  • Publish Date: 2010-08-15
  • Bifurcation properties of Duffing-van der Pol System with two parameters under multi-frequency excitations were studied. It was discussed for three cases 1 λ1 was considered as bifurcation parameter, 2 λ2 was considered as bifurcation parameter, 3 λ1 and λ2 were both considered as bifurcation parameters. According to the definition of transition sets, the whole parametric space was divided into several different persistent regions by the transition sets for different cases. The bifurcation diagrams in different persistent regions were obtained, which could provide a theoretical basis for optmial design of the system.
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