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Bifurcations and Chaos in Duffing Equation with Damping and External Excitations

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文摘 Duffing equation with damping and external excitations is investigated. By using Melnikov method and bifurcation theory, the criterions of existence of chaos under periodic perturbations are obtained. By using second-order averaging method, the criterions of existence of chaos in averaged system under quasi-periodic perturbations for = nω + εσ, = 2, 4, 6 (where σ is not rational to ω) are investigated. However, the criterions of existence of chaos for n = 1, 3, 5, 7 ? 20 can not be given. The numerical simulations verify the theoretical analysis, show the occurrence of chaos in the averaged system and original system under quasi- periodic perturbation for n = 1, 2, 3, 5, and expose some new complex dynamical behaviors which can not be given by theoretical analysis. In particular, the dynamical behaviors under quasi-periodic perturbations are different from that under periodic perturbations, and the period-doubling bifurcations to chaos has not been found under quasi-periodic perturbations.
来源 Acta Mathematicae Applicatae Sinica-English Series ,2014,30(2):483-504 【核心库】
DOI 10.1007/s10255-014-0284-0
关键词 Duffing equation ; Melnikov method ; second-order averaging method ; chaos
地址

1. Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha, 410004  

2. College of Science, China Agriculture University, Beijing, 100083  

3. Department of Mathematics and Physics, Hunan Institute of Engineering, Xiangtan, 411104

语种 英文
文献类型 研究性论文
ISSN 0168-9673
学科 力学;物理学
基金 国家自然科学基金 ;  湖南省自然科学基金 ;  talent introduction fund
文献收藏号 CSCD:5102549

参考文献 共 26 共2页

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引证文献 2 篇

1 吴彦华 内置频率对Duffing振子微弱二进制相移键控信号盲检测影响 国防科技大学学报,2019,41(1):80-88
CSCD被引 0 次

2 Zhou Liangqiang Chaotic Motions of the van der Pol-Duffing Oscillator Subjected to Periodic External and Parametric Excitations with Delayed Feedbacks Acta Mathematicae Applicatae Sinica-English Series,2024,40(4):1111-1126
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