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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.
[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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[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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