Sub-harmonic Resonance Solutions of Generalized Strongly Nonlinear Van der Pol Equation with Parametric and External Excitations

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  • Jincheng college, Nanjing University of Aeronautics and Astronautics
XU Dong-liang(1979-), male, native of Zhoukou, Henan, a lecturer of Nanjing University of Aeronautics and Astronautics, Ph.D., engages in management Science and engineering.

Received date: 2017-07-06

  Online published: 2020-10-23

Supported by

Supported by the National Natural Science Foundation of China(11201118);

Abstract

In this paper a modified L-P method and multiple scale method are used to solve sub-harmonic resonance solutions of strong and nonlinear resonance of general Van der Pol equation with parametric and external excitations by parametric transformation. Bifurcation response equation and transition sets of sub-harmonic resonance with strong nonlinearity of general Van der Pol equation with parametric and external excitation are worked out.Besides, transition sets and bifurcation graphs are drawn to help to analysis the problems theoretically. Conclusions show that the transition sets of general and nonlinear Van der Pol equation with parametric and external excitations are more complex than those of general and nonlinear Van der Pol equation only with parametric excitation, which is helpful for the qualitative and quantitative reference for engineering and science applications. 

Cite this article

XU Dong-liang . Sub-harmonic Resonance Solutions of Generalized Strongly Nonlinear Van der Pol Equation with Parametric and External Excitations[J]. Chinese Quarterly Journal of Mathematics, 2017 , 32(3) : 322 -330 . DOI: 10.13371/j.cnki.chin.q.j.m.2017.03.010

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