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研究Duffing振子系统的周期解的唯一性与精确周期信号的获取方法. 应用定性分析方法,获得了一类Duffing振子系统具有唯一周期解的必要条件,同时也得到了一类更广泛的非线性周期系统的周期解的唯一性.在一定条件下,给出了Duffing振子系统精确周期信号的获取方法.
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关键词:
- Duffing振子系统 /
- 周期解的唯一性 /
- 精确周期信号的获取方法
The acquisition method of precise periodic signal and uniqueness of periodic solutions of Duffing oscillator system is investigated. The necessary condition of uniqueness of periodic solutions of a kind of Duffing oscillator system is presented and the uniqueness of periodic solutions of some extensive nonlinear periodic system is simultaneously obtained by using qualitative analysis method .The acquisition method of precise periodic signal Duffing oscillator system is given under certain conditions.-
Keywords:
- Duffing oscillator system /
- uniqueness of periodic solutions /
- acquisition method of precise periodic signal
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[2] Liu Z R 1994 Perturbation Criteria for Chaos (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [刘曾荣 1994 混沌的微扰判据 (上海: 上海科技教育出版社) ]
[3] Liu S K, Liu S D, Tan B K 1996 Nonlinear Atmospheric Dynamics (Beijing: National Defense Industry Press) (in Chinese) [刘式适、 刘式达、 谭本馗 1996 非线性大气动力学 (北京: 国防工业出版社) ] 〖4] Liu Y Z, Chen L Q 2003 Nonlinear Vibrations (Beijing: High Education Press) (in Chinese)[刘延柱、 陈立群 2003 非线性振动 (北京: 高等教育出版社)]
[4] Marinca V, Herisanu N 2008 Chaos Soliton. Fractals 37 114
[5] Srinivasan K, Thamilmaran K, Venkatesan A 2009 Chaos Soliton. Fract. 40 319
[6] Li Y, Xu K, Yang B J, Yuan Y 2008 Acta Phys. Sin. 57 3344 (in Chinese) [李 月、 徐 凯、 杨宝俊、 袁 野 2008 57 3344 ]
[7] Li Y, Lu P, Yang B J, Zhao P X 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李 月、 路 鹏、 杨宝俊、 赵雪平 2006 55 1672]
[8] Wang G Y, Zheng W, He S L 2002 Signal Process. 82 103
[9] Wang G Y, He S L 2003 IEEE Trans. Circ. Syst. 50 945
[10] Chen L, Wang D S 2007 Acta Phys. Sin. 56 5098 (in Chinese)[谌 龙、 王德石 2007 56 5098 ]
[11] Xing H Y, Xu W 2007 Acta Phys. Sin. 56 3771 (in Chinese) [行鸿彦、 徐 伟 2007 56 3771]
[12] Schilling R J, Robert J C, James J 2001 IEEE Trans. Neural Networks 12 1
[13] Henry H 2000 IEEE Trans. Neural Networks 5 1131
[14] Guo H J, Liu J H 2004 Acta Phys . Sin. 53 4080 (in Chinese) [郭会军、 刘君华 2004 53 4080]
[15] Kong Z Q, Liu D, Ren H P 2003 Acta Phys. Sin. 52 531 ( in Chinese) [孔志强、 刘 丁、 任海鹏 2003 52 531]
[16] Wu F L, Shi Z K, Yang X H 2007 J. Ship. Mech. 11 136 (in Chinese) [吴方良、 石仲堃、 杨向晖 2007 船舶力学 11 136]
[17] Li Y, Yang B J, Lin H B, Liu X H 2005 Acta Phys. Sin. 54 1994 (in Chinese) [李 月、 杨宝俊、 林红波、 刘晓华 2005 54 1994 ]
[18] Sansone G, Conti R 1983 Nonlinear Differential Equations (Beijing: Science Press) (in Chinese) [中译本]
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[1] Guckenheimer J, Holmes P 1983 Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields (New York: Springer-Verlag Press)
[2] Liu Z R 1994 Perturbation Criteria for Chaos (Shanghai: Shanghai Scientific and Technological Education Publishing House) (in Chinese) [刘曾荣 1994 混沌的微扰判据 (上海: 上海科技教育出版社) ]
[3] Liu S K, Liu S D, Tan B K 1996 Nonlinear Atmospheric Dynamics (Beijing: National Defense Industry Press) (in Chinese) [刘式适、 刘式达、 谭本馗 1996 非线性大气动力学 (北京: 国防工业出版社) ] 〖4] Liu Y Z, Chen L Q 2003 Nonlinear Vibrations (Beijing: High Education Press) (in Chinese)[刘延柱、 陈立群 2003 非线性振动 (北京: 高等教育出版社)]
[4] Marinca V, Herisanu N 2008 Chaos Soliton. Fractals 37 114
[5] Srinivasan K, Thamilmaran K, Venkatesan A 2009 Chaos Soliton. Fract. 40 319
[6] Li Y, Xu K, Yang B J, Yuan Y 2008 Acta Phys. Sin. 57 3344 (in Chinese) [李 月、 徐 凯、 杨宝俊、 袁 野 2008 57 3344 ]
[7] Li Y, Lu P, Yang B J, Zhao P X 2006 Acta Phys. Sin. 55 1672 (in Chinese) [李 月、 路 鹏、 杨宝俊、 赵雪平 2006 55 1672]
[8] Wang G Y, Zheng W, He S L 2002 Signal Process. 82 103
[9] Wang G Y, He S L 2003 IEEE Trans. Circ. Syst. 50 945
[10] Chen L, Wang D S 2007 Acta Phys. Sin. 56 5098 (in Chinese)[谌 龙、 王德石 2007 56 5098 ]
[11] Xing H Y, Xu W 2007 Acta Phys. Sin. 56 3771 (in Chinese) [行鸿彦、 徐 伟 2007 56 3771]
[12] Schilling R J, Robert J C, James J 2001 IEEE Trans. Neural Networks 12 1
[13] Henry H 2000 IEEE Trans. Neural Networks 5 1131
[14] Guo H J, Liu J H 2004 Acta Phys . Sin. 53 4080 (in Chinese) [郭会军、 刘君华 2004 53 4080]
[15] Kong Z Q, Liu D, Ren H P 2003 Acta Phys. Sin. 52 531 ( in Chinese) [孔志强、 刘 丁、 任海鹏 2003 52 531]
[16] Wu F L, Shi Z K, Yang X H 2007 J. Ship. Mech. 11 136 (in Chinese) [吴方良、 石仲堃、 杨向晖 2007 船舶力学 11 136]
[17] Li Y, Yang B J, Lin H B, Liu X H 2005 Acta Phys. Sin. 54 1994 (in Chinese) [李 月、 杨宝俊、 林红波、 刘晓华 2005 54 1994 ]
[18] Sansone G, Conti R 1983 Nonlinear Differential Equations (Beijing: Science Press) (in Chinese) [中译本]
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