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针对一类周期参数扰动的T混沌系统, 通过变换将系统转化为具有广义Hamilton结构的周期参数扰动的慢变系统, 运用Melnikov方法对系统的同宿轨道进行了分析计算, 并给出了系统的同宿轨道参数分支条件. 同时, 通过数值实验, 对周期参数扰动控制策略及同宿轨道进行了仿真, 验证了文中理论分析的正确性.
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关键词:
- Hamilton系统 /
- Melnikov方法 /
- 同宿轨道 /
- 周期参数扰动
[1] Živković T, Rypdal K 2008 Phys. Rev. E 77 037401
[2] Lv J H, Chen G R 2006 International Journal of bifurcation and chaos 16 775
[3] Wang Z, Sun W, Wei Z C 2012 Advanced Materials Research 486 204
[4] Wang Z 2011 Control Theory & Applications 28 1036 (in Chinese) [王震 2011 控制理论与应用 28 1036]
[5] Ling B W K, Iu H H C, Lam H K 2008 Control of Chaos in Nonlinear Circuits and Systems (Singapore: World Sciectific Publishing Co. Pte. Ltd) p35
[6] Wang Z, Li Y X, Xi X J, Lv L 2011 Acta Phys. Sin. 60 010513 (in Chinese) [王震, 李永新, 惠小健, 吕雷 2011 物理学报 60 010513]
[7] Wang Z, Wu Y T, Li Y X, Zou Y J 2009 Proceedings of the 4th International Conference on Computer Science and Education Nanning, China, July 25-28, 2009, p441
[8] Fang Y Y, Xu Z Y, Cai C H 2001 Journal of Wuxi University of light industry 20 624 (in Chinese) [方燕燕, 徐振源, 蔡朝洪 2001 无锡轻工大学学报 20 624]
[9] Wei Z C, Yang Q G 2009 Computers & Mathematics with Applications 58 1979
[10] Wu Z M, Xie J Y, Fang Y Y, Xu Z Y 2007 Chaos Solitons & Fractals 32 104
[11] Min F H, Xu W B, Xu Z Y 2002 Acta Phys. Sin. 51 1690 (in Chinese) [闵富红, 须文波, 徐振源 2002 物理学报 51 1690]
[12] Yang X L, Xu W, Sun Z K 2006 Acta Phys. Sin. 55 1678 (in Chinese) [杨晓丽, 徐伟, 孙中奎 2006 物理学报 55 1678]
[13] Sprott J C 1994 Phys. Rev. E 50 647
[14] Yang Q G, Chen G R 2008 International Journal of Bifurcation and chaos 18 1393
[15] Wang Z 2010 Nonlinear Dynamics 60 369
[16] Tigan G H 2005 Scientific Bulletin of the politehnica University of Timisoara 50 61
[17] Mirus K A, Sprott J C 1999 Phys. Rev. E 59 5313
[18] Mirus K A, Sprott J C 1999 Phys. Lett. A 254 275
[19] Li J B, Zhao X H, Liu Z R 2007 Theory of generalized Hamilton system and its applications (Beijing: Science Press) p140 (in Chinese) [李继彬, 赵晓华, 刘正荣 2007 广义哈密顿系统理论及其应用 (北京: 科学出版社) 第140页]
[20] Wiggins S, Holmes P 1987 SIAM Journal on mathematical Analysis 18 612
[21] Liu Z R 2004 Perturbation criteria for chaos (Shanghai: Shanghai scientific and technological education publishing house) p74 (in Chinese) [刘曾荣 2004 混沌的微扰判据 (上海: 上海科技教育出版社) 第74页]
-
[1] Živković T, Rypdal K 2008 Phys. Rev. E 77 037401
[2] Lv J H, Chen G R 2006 International Journal of bifurcation and chaos 16 775
[3] Wang Z, Sun W, Wei Z C 2012 Advanced Materials Research 486 204
[4] Wang Z 2011 Control Theory & Applications 28 1036 (in Chinese) [王震 2011 控制理论与应用 28 1036]
[5] Ling B W K, Iu H H C, Lam H K 2008 Control of Chaos in Nonlinear Circuits and Systems (Singapore: World Sciectific Publishing Co. Pte. Ltd) p35
[6] Wang Z, Li Y X, Xi X J, Lv L 2011 Acta Phys. Sin. 60 010513 (in Chinese) [王震, 李永新, 惠小健, 吕雷 2011 物理学报 60 010513]
[7] Wang Z, Wu Y T, Li Y X, Zou Y J 2009 Proceedings of the 4th International Conference on Computer Science and Education Nanning, China, July 25-28, 2009, p441
[8] Fang Y Y, Xu Z Y, Cai C H 2001 Journal of Wuxi University of light industry 20 624 (in Chinese) [方燕燕, 徐振源, 蔡朝洪 2001 无锡轻工大学学报 20 624]
[9] Wei Z C, Yang Q G 2009 Computers & Mathematics with Applications 58 1979
[10] Wu Z M, Xie J Y, Fang Y Y, Xu Z Y 2007 Chaos Solitons & Fractals 32 104
[11] Min F H, Xu W B, Xu Z Y 2002 Acta Phys. Sin. 51 1690 (in Chinese) [闵富红, 须文波, 徐振源 2002 物理学报 51 1690]
[12] Yang X L, Xu W, Sun Z K 2006 Acta Phys. Sin. 55 1678 (in Chinese) [杨晓丽, 徐伟, 孙中奎 2006 物理学报 55 1678]
[13] Sprott J C 1994 Phys. Rev. E 50 647
[14] Yang Q G, Chen G R 2008 International Journal of Bifurcation and chaos 18 1393
[15] Wang Z 2010 Nonlinear Dynamics 60 369
[16] Tigan G H 2005 Scientific Bulletin of the politehnica University of Timisoara 50 61
[17] Mirus K A, Sprott J C 1999 Phys. Rev. E 59 5313
[18] Mirus K A, Sprott J C 1999 Phys. Lett. A 254 275
[19] Li J B, Zhao X H, Liu Z R 2007 Theory of generalized Hamilton system and its applications (Beijing: Science Press) p140 (in Chinese) [李继彬, 赵晓华, 刘正荣 2007 广义哈密顿系统理论及其应用 (北京: 科学出版社) 第140页]
[20] Wiggins S, Holmes P 1987 SIAM Journal on mathematical Analysis 18 612
[21] Liu Z R 2004 Perturbation criteria for chaos (Shanghai: Shanghai scientific and technological education publishing house) p74 (in Chinese) [刘曾荣 2004 混沌的微扰判据 (上海: 上海科技教育出版社) 第74页]
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