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Using Melnikov method we have analysed and calculated the homoclinic orbits of a slowly varying oscillator, derived from the T chaotic system with generalized Hamiltonian structure under periodic parametric perturbation. Also the parameter bifurcation conditions of homoclinic orbits are obtained. The simulation results demonstrate the feasibility of periodic parametric perturbation control technology, and the correctness of the discussion in this paper.
[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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[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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