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Bifurcation and resonance of fractional cubic nonlinear system

Author

Listed:
  • Xie, Jiaquan
  • Zhao, Fuqiang
  • He, Dongping
  • Shi, Wei

Abstract

In this paper, the dynamic characteristics of a class of fractional cubic nonlinear systems are studied. Firstly, the analytical expressions of amplitude-frequency relationship of forced vibration system are obtained by means of average method, and then compared with the numerical solutions defined by Grünwald-Letnikov fractional differential. Secondly, the amplitude-frequency characteristic curves of the forced vibration system under different fractional orders, external excitation amplitude, cubic stiffness and fractional differential terms were investigated respectively. Thirdly, the amplitude-frequency and phase-frequency characteristics of self-excited vibration system under different fractional orders are investigated. Finally, the fork bifurcation behavior of the system under different external excitation amplitudes, cubic damping and fractional differential terms is analyzed. In addition, the change of equilibrium point caused by fractional order under different fractional differential terms and cubic damping and the saddle node bifurcation caused by the change of cubic damping parameters are also analyzed.

Suggested Citation

  • Xie, Jiaquan & Zhao, Fuqiang & He, Dongping & Shi, Wei, 2022. "Bifurcation and resonance of fractional cubic nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002636
    DOI: 10.1016/j.chaos.2022.112053
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