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| Bifurcations and Chaos in Duffng Equation with Damping and External Excitations | |
| 作者姓名： | Mei-xiang CAI Jian-ping YANG Jin DENG |
| 基金项目： | Supported by the National Natural Science Foundation of China （No. 10801135,11101170） and Hunan Provincial Natural Science Foundation of China （No. 13JJ4088）, talent introduction fund （No. 104-0163）. |
| 摘 要： | Duffng 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 forff=nω+εσ,n=2,4,6(whereσis not rational toω)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 quasiperiodic 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. |
| 关 键 词： | Duffing振子 倍周期分岔 混沌 激励 阻尼 Melnikov方法 准周期扰动 动力学行为 |
Bifurcations and chaos in Duffing equation with damping and external excitations |
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| Mei-xiang CAI,Jian-ping YANG,Jin DENG.Bifurcations and Chaos in Duffng Equation with Damping and External Excitations[J].Acta Mathematicae Applicatae Sinica,2014,30(2):483-504. | |
| Authors: | Mei-xiang Cai Jian-ping Yang Jin Deng |
| Institution: | 1. Institute of Mathematics and Physics, Central South University of Forestry and Technology, Changsha, 410004, China 2. College of Science, China Agriculture University, Beijing, 100083, China 3. Department of Mathematics and Physics, Hunan Institute of Engineering, Xiangtan, 411104, China |
| Abstract: | Duffing equation Melnikov method second-order averaging method chaos |
| Keywords: | Duffing equation Melnikov method second-order averaging method chaos |
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