Jerk系统耦合的分岔和混沌行为

陈章耀; 毕勤胜

doi:10.7498/aps.59.7669

摘要

通过分析耦合的Jerk系统的平衡点及其稳定性,给出了参数空间中不同的分岔集,进而将参数空间划分为对应于各种动力学行为的不同区域.探讨了耦合系统随不同参数变化的动力学演化过程,重点分析了系统耦合强度变化对其动力学行为的影响.揭示了多种运动模式共存及倍周期分岔等各种非线性现象的产生机理.

关键词:

Jerk系统 /
耦合 /
分岔 /
共存

Upon the analysis of the equilibrium points as well as the stabilities in coupled Jerk systems, bifurcation sets in parameter space are derived, which divide the parameter space into several regions associated with different forms of dynamics. The dynamical evolution of the coupled system is investigated with the variation of different parameters and specially, the influence of the coupling strength on the dynamics of the system is explored in details. The mechanism of some nonlinear phenomena such as the coexistence of multiple behaviors as well as the sequence of period-doubling bifurcations are presented.

Keywords:

Jerk system /
couple /
bifurcation /
coexistence

作者及机构信息

1.
江苏大学理学院,镇江 212013

基金项目: 国家自然科学基金 (批准号:10872080,10972091) 和江苏大学高级人才基金(批准号:10JDG062)资助的课题.

Authors and contacts

1.
Faculty of Science, Jiangsu University, Zhenjiang 212013, China

参考文献

[1]	Maccari A 2001 Int. J. Nonlin. Mech. 36 335
[2]	Yu H J, Liu Y Z 2005 Acta Phy. Sin. 54 3029 (in Chinese)[于洪洁、刘延柱 2005 物理学报 54 3029]
[3]	Liu M H, Yu S M 2006 Acta Phy. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 物理学报 55 5707 Sprott J C 2000 Amer. J. Phys. 68 758 〖5] Malasoma J M 2009 Chaos, Solitons and Fractals 39 533
[4]	Chlouverakis K E, Sprott J C 2006 Chaos, Solitons and Fractals 28 739
[5]	Maccari A 1998 Nonlinear Dynamics 15 329
[6]	Liu Y 2009 Acta Phys. Sin. 58 0749 (in Chinese) [刘勇 2009 物理学报 58 749]
[7]	Roman A F, Alexander E H, Alexey A K 2006 Phys. Lett. A 358 301
[8]	Agiza H N, Matouk A E 2006 Chaos, Solitons and Fractals 28 219
[9]	Bi Q 2004 Int.l J. Nonlin. Mech. 39 33
[10]	Bi Q 2004 Int. J. Bifur. Chaos 14 337
[11]	Zhang Z D, Bi Q 2005 Int. J. Nonlin. Sci. Num. Simul. 6 81
[12]	Zhang Z D, Bi Q 2005 Chaos, Solitons and Fractals 23 1185

施引文献

[1]	Maccari A 2001 Int. J. Nonlin. Mech. 36 335
[2]	Yu H J, Liu Y Z 2005 Acta Phy. Sin. 54 3029 (in Chinese)[于洪洁、刘延柱 2005 物理学报 54 3029]
[3]	Liu M H, Yu S M 2006 Acta Phy. Sin. 55 5707 (in Chinese) [刘明华、禹思敏 2006 物理学报 55 5707 Sprott J C 2000 Amer. J. Phys. 68 758 〖5] Malasoma J M 2009 Chaos, Solitons and Fractals 39 533
[4]	Chlouverakis K E, Sprott J C 2006 Chaos, Solitons and Fractals 28 739
[5]	Maccari A 1998 Nonlinear Dynamics 15 329
[6]	Liu Y 2009 Acta Phys. Sin. 58 0749 (in Chinese) [刘勇 2009 物理学报 58 749]
[7]	Roman A F, Alexander E H, Alexey A K 2006 Phys. Lett. A 358 301
[8]	Agiza H N, Matouk A E 2006 Chaos, Solitons and Fractals 28 219
[9]	Bi Q 2004 Int.l J. Nonlin. Mech. 39 33
[10]	Bi Q 2004 Int. J. Bifur. Chaos 14 337
[11]	Zhang Z D, Bi Q 2005 Int. J. Nonlin. Sci. Num. Simul. 6 81
[12]	Zhang Z D, Bi Q 2005 Chaos, Solitons and Fractals 23 1185

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