耦合发电机系统的分岔和双参数特性

吴淑花; 孙毅; 郝建红; 许海波

doi:10.7498/aps.60.010507

摘要

在综合分析系统基本动力学特性的基础上,通过数值计算Lyapunov指数谱、分岔图等,讨论了耦合发电机系统的混沌分岔行为和周期窗口的性态变化;计算和分析了系统在二维参数空间的双参数特性.结果显示系统在倍周期分岔中会出现缺边现象,在双参数空间系统出现复杂的分岔结构,两个控制参数对系统动力学行为的影响特性有所差别.

关键词:

Based on the comprehensive analysis of the basic dynamic characters of the coupled dynamos system, we have calculated the Lyapunov exponent spectra, bifurcation diagrams and so on, and discussed the chaotic bifurcation and mutative characteristic thoroughly in the periodic windows of the system, and the dual-parameter characteristic is also analyzed. It is found that a boundary line is absent in period-doubling bifurcations and a complicated bifurcation structure appears in 2D parameter space, the influences of two control parameters to the dynamic behavior are different.

Keywords:

作者及机构信息

(1)北京应用物理与计算数学研究所,北京 100088; (2)华北电力大学电气与电子工程学院,北京 102206; (3)华北电力大学电气与电子工程学院,北京 102206;石家庄学院物理与电气信息工程系,石家庄 050035

基金项目: 华北电力大学博士基金(批准号:kH0433)和国际科技合作项目(批准号:2007DFA71250)资助的课题.

Authors and contacts

(1)Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; (2)School of Electric and Electronic Engineering, North China Electric Power University, Beijing 102206, China; (3)School of Electric and Electronic Engineering, North China Electric Power University, Beijing 102206, China;Department of Physics and Electrical Information Engineering, Shijiazhuang Normal College, Shijiazhuang 050035, China

参考文献

[1]	Kennedy M P 1993 IEEE Trans. Circ. Syst. I 40 657
[2]	Matias M A, Guemez J 1994 Phys. Rev. Lett. 72 1455
[3]	Liu Y, Barbosa L C, Riosleite J R 1994 Phys. Rev. Lett. A 193 259
[4]	Liu B Z, Peng J H 2004 Nonlinear Dynamics (BeiJing: Higher Education Press) p317 (in Chinese) [刘秉正、彭建华2004 非线性动力学(北京:高等教育出版社)第317 页]
[5]	Agiza H N 2002 Chaos, Solitons & Fractals 13 341
[6]	Li S H, Tian Y P 2003 Chaos, Solitons & Fractals 16 787
[7]	Awad E G, Rizk Y 2006 Chaos, Solitons & Fractals 29 1085
[8]	Wang X D, Tian L X 2004 Chaos, Solitons & Fractals 21 193
[9]	Mahmoud G M, Aly S A, Farghaly A A 2007 Chaos, Solitons & Fractals 33 178
[10]	Agiza H N 2004 Int. J. Modern Phys. C 15 873
[11]	Wang X Y, Wu X J 2006 Acta Phys. Sin. 55 5083 (in Chinese) [王兴元、武相军 2006 物理学报 55 5083 ]
[12]	Zhang X F, Chen Z Y, Bi Q S 2009 Acta Phys. Sin. 58 2963 (in Chinese) [张晓芳、陈章耀、毕勤胜 2009 物理学报 58 2963]
[13]	Luo S Y, Shao M Z, Luo X H 2010 Acta Phys. Sin.59 2685 (in Chinese) [罗诗裕、邵明珠、罗晓华 2010 物理学报 59 2685]
[14]	Yu J J, Cao H F, Xu H B, Xu Q 2006 Acta Phys. Sin. 55 29 (in Chinese) [于津江、曹鹤飞、许海波、徐权 2006 物理学报 55 29]
[15]	Zhang Y, Lei Y M, Fang T 2009 Acta Phys. Sin. 58 3799 (in Chinese) [张莹、雷佑铭、方同 2009 物理学报 58 3799]
[16]	Yang S Q, Zhang X H, Zhao C A 2000 Acta Phys. Sin. 49 636 (in Chinese) [杨绍清、张新华、赵长安 2000 物理学报 49 636]
[17]	Rasband S N 1990 Chaotic Dynamics (New York: John Wiley & Sons) p36

施引文献

[1]	Kennedy M P 1993 IEEE Trans. Circ. Syst. I 40 657
[2]	Matias M A, Guemez J 1994 Phys. Rev. Lett. 72 1455
[3]	Liu Y, Barbosa L C, Riosleite J R 1994 Phys. Rev. Lett. A 193 259
[4]	Liu B Z, Peng J H 2004 Nonlinear Dynamics (BeiJing: Higher Education Press) p317 (in Chinese) [刘秉正、彭建华2004 非线性动力学(北京:高等教育出版社)第317 页]
[5]	Agiza H N 2002 Chaos, Solitons & Fractals 13 341
[6]	Li S H, Tian Y P 2003 Chaos, Solitons & Fractals 16 787
[7]	Awad E G, Rizk Y 2006 Chaos, Solitons & Fractals 29 1085
[8]	Wang X D, Tian L X 2004 Chaos, Solitons & Fractals 21 193
[9]	Mahmoud G M, Aly S A, Farghaly A A 2007 Chaos, Solitons & Fractals 33 178
[10]	Agiza H N 2004 Int. J. Modern Phys. C 15 873
[11]	Wang X Y, Wu X J 2006 Acta Phys. Sin. 55 5083 (in Chinese) [王兴元、武相军 2006 物理学报 55 5083 ]
[12]	Zhang X F, Chen Z Y, Bi Q S 2009 Acta Phys. Sin. 58 2963 (in Chinese) [张晓芳、陈章耀、毕勤胜 2009 物理学报 58 2963]
[13]	Luo S Y, Shao M Z, Luo X H 2010 Acta Phys. Sin.59 2685 (in Chinese) [罗诗裕、邵明珠、罗晓华 2010 物理学报 59 2685]
[14]	Yu J J, Cao H F, Xu H B, Xu Q 2006 Acta Phys. Sin. 55 29 (in Chinese) [于津江、曹鹤飞、许海波、徐权 2006 物理学报 55 29]
[15]	Zhang Y, Lei Y M, Fang T 2009 Acta Phys. Sin. 58 3799 (in Chinese) [张莹、雷佑铭、方同 2009 物理学报 58 3799]
[16]	Yang S Q, Zhang X H, Zhao C A 2000 Acta Phys. Sin. 49 636 (in Chinese) [杨绍清、张新华、赵长安 2000 物理学报 49 636]
[17]	Rasband S N 1990 Chaotic Dynamics (New York: John Wiley & Sons) p36

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