| GLOBAL BIFURCATION AND CHAOS IN A VAN DER POL-DUFFING-MATHIUE SYSTEM WITH A SINGLE-WELL POTENTIAL OSCILLATOR |
| |
| 引用本文： | Xu Jian,Wang Cheng,Department of Mechanics,Huazhong University of Science & Technology,Wuhan 430074,ChinaChen Yushu,Department of Mechanics,Tainjin University,Tianjin 300072,ChinaLu Qishao,Department of Applied Mathematics and Physics,Beijing University of Aeronautics and Astronautics,Beijing 100083,China. GLOBAL BIFURCATION AND CHAOS IN A VAN DER POL-DUFFING-MATHIUE SYSTEM WITH A SINGLE-WELL POTENTIAL OSCILLATOR[J]. Acta Mechanica Solida Sinica, 1997, 10(3): 262-275. DOI: 10.1007/BF02208076 |
| |
| 作者姓名： | Xu Jian Wang Cheng Department of Mechanics Huazhong University of Science & Technology Wuhan 430074 ChinaChen Yushu Department of Mechanics Tainjin University Tianjin 300072 ChinaLu Qishao Department of Applied Mathematics and Physics Beijing University of Aeronautics and Astronautics Beijing 100083 China |
| |
| 作者单位： | Xu Jian;Wang Cheng，Department of Mechanics，Huazhong University of Science & Technology，Wuhan 430074，ChinaChen Yushu，Department of Mechanics，Tainjin University，Tianjin 300072，ChinaLu Qishao，Department of Applied Mathematics and Physics，Beijing University of Aeronautics and Astronautics，Beijing 100083，China |
| |
| 基金项目： | The subject is supported by NNSF and PSF of China |
| |
| 摘 要： | The global bifurcation and chaos are investigated in this paper for a van der Pol-Duff-ing-Mathieu system with a single-well potential oscillator by means of nonlinear dynamics. The au-tonomous system corresponding to the system under discussion is analytically studied to draw all globalbifureation diagrams in every parameter space, These diagrams are called basic bifurcation ones. Thenfixing parameter in every space and taking the parametrically excited amplitude as a bifurcation param-eter, we can observe how to evolve from a basic bifurcation diagram to a chaos pattern in terms of nu-merical methods. The results are sufficient to show that the system has distinct dynamic behavior, Fi-nally, the properties of the basins of attraction are observed and the appearance of fractal basin bound-aries heralding the onset of a loss of structural integrity is noted in order to consider how to control theextent and the rate of the erosion in the next paper.
|
| 收稿时间： | 1997-05-15 |
GLOBAL BIFURCATION AND CHAOS IN A VAN DER POL-DUFFING-MATHIUE SYSTEM WITH A SINGLE-WELL POTENTIAL OSCILLATOR |
| |
| Xu Jian,Wang Cheng. GLOBAL BIFURCATION AND CHAOS IN A VAN DER POL-DUFFING-MATHIUE SYSTEM WITH A SINGLE-WELL POTENTIAL OSCILLATOR[J]. Acta Mechanica Solida Sinica, 1997, 10(3): 262-275. DOI: 10.1007/BF02208076 |
| |
| Authors: | Xu Jian Wang Cheng |
| |
| Affiliation: | (1) Department of Mechanics, Huazhong University of Science & Technology, 430074 Wuhan, China;(2) Department of Mechanics, Tainjin University, 300072 Tianjin, China;(3) Department of Applied Mathematics and Physics, Beijing University of Aeronautics and Astronautics, 100083 Beijing, China |
| |
| Abstract: | The global bifurcation and chaos are investigated in this paper for a van der Pol-Duff- ing-Mathieu system with a single-well potential oscillator by means of nonlinear dynamics. The au- tonomous system corresponding to the system under discussion is analytically studied to draw all global bifureation diagrams in every parameter space, These diagrams are called basic bifurcation ones. Then fixing parameter in every space and taking the parametrically excited amplitude as a bifurcation param- eter, we can observe how to evolve from a basic bifurcation diagram to a chaos pattern in terms of nu- merical methods. The results are sufficient to show that the system has distinct dynamic behavior, Fi- nally, the properties of the basins of attraction are observed and the appearance of fractal basin bound- aries heralding the onset of a loss of structural integrity is noted in order to consider how to control the extent and the rate of the erosion in the next paper. |
| |
| Keywords: | global bifurcation chaos nonlinear vibration basin fractal |
| 本文献已被 CNKI SpringerLink 等数据库收录！ |
