Bifurcation and resonance of fractional cubic nonlinear system

Jiaquan Xie, Fuqiang Zhao, Dongping He and Wei Shi

Chaos, Solitons & Fractals, 2022, vol. 158, issue C

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.

Keywords: Fractional order; Resonance; Bifurcation; Response; Average method (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922002636
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002636

DOI: 10.1016/j.chaos.2022.112053

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().