一个基于Chen系统的新混沌系统的分析与同步

张国山; 牛弘

doi:10.7498/aps.61.110503

摘要

通过在Chen系统的第一个方程中加入一个可变系数的乘积项, 构造了一个新的三维自治混沌系统.新系统可通过调节其可变系数实现不同系数组合下系统的混沌产生或混沌抑制, 即调节该乘积项的可变系数, 可使不出现混沌的Chen系统产生混沌现象, 同时也可使产生混沌运动的Chen系统不再产生混沌现象.详细分析了新系统的特性, 研究了新系统的混沌同步问题, 并给出了相应的仿真结果.

关键词:

In this paper, a new three-dimensional autonomous chaotic system is constructed by adding a product term with variable coefficient to the first equation of Chen's system. The new system with different groups of coefficients can be chaotic or not by adjusting the variable coefficient, that is, by adjusting the variable coefficient, chaos occurs in new system when Chen's system is not chaotic, or chaos is suppressed in new system even if Chen's system is chaotic. The characteristics of the new chaotic system are analyzed in detail and the synchronization of new system is considered. Moreover, the simulation results are also presented.

Keywords:

Chen's system /
the new three-dimensional autonomous chaotic system /
chaos suppression /
synchronization

作者及机构信息

张国山,
牛弘

1.
天津大学电气与自动化工程学院, 天津 300072

基金项目: 国家自然科学基金(批准号: 61074088) 资助的课题.

Authors and contacts

1.
School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61074088).

参考文献

[1]	Liu B Z, Peng J H 2007 Nonlinear Dynamics (Beijing: Higher Education Press) pp120--131 (in Chinese) [刘秉正, 彭建华 2007 非线性动力学 (北京: 高等教育出版社) 第120---131页]
[2]
[3]	Chen G R, L J H 2003 Dynamic Analysis, Control and Synchronization of Lorenz System Families (Beijing: Science Press) pp9--130 (in Chinese) [陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京: 科学出版社) 第9---130页]
[4]
[5]	Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[6]	L J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[7]
[8]	L J H, Chen G R, Cheng D Z, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[9]
[10]
[11]	Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[12]
[13]	Wang F Z, Qi G Y, Chen Z Q, Zhang Y H, Yuan Z Z 2006 Acta Phys. Sin. 55 4005 (in Chinese) [王繁珍, 齐国元, 陈增强, 张宇辉, 袁著祉 2006 物理学报 55 4005]
[14]
[15]	Liu C X, Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[16]	Tomasz K (translated by Shi Y) 2008 Chaos for Engineers: Theory, Application, and Control (2nd Ed.) ( Beijing: National Defense Industry Press) p62 (in Chinese) [卡毕坦尼亚克著 (施引译) 2008 面向工程的混沌学-----理论、应用及控制(第2版) (北京: 国防工业出版社) 第62页]
[17]
[18]
[19]	Zhong G Q, Tang W K S 2002 Int. J. Bifur. Chaos 12 1423
[20]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[21]

施引文献

[1]	Liu B Z, Peng J H 2007 Nonlinear Dynamics (Beijing: Higher Education Press) pp120--131 (in Chinese) [刘秉正, 彭建华 2007 非线性动力学 (北京: 高等教育出版社) 第120---131页]
[2]
[3]	Chen G R, L J H 2003 Dynamic Analysis, Control and Synchronization of Lorenz System Families (Beijing: Science Press) pp9--130 (in Chinese) [陈关荣, 吕金虎 2003 Lorenz系统族的动力学分析、控制与同步 (北京: 科学出版社) 第9---130页]
[4]
[5]	Chen G R, Ueta T 1999 Int. J. Bifur. Chaos 9 1465
[6]	L J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[7]
[8]	L J H, Chen G R, Cheng D Z, Celikovsky S 2002 Int. J. Bifur. Chaos 12 2917
[9]
[10]
[11]	Qi G Y, Chen G R, Du S Z, Chen Z Q, Yuan Z Z 2005 Physica A 352 295
[12]
[13]	Wang F Z, Qi G Y, Chen Z Q, Zhang Y H, Yuan Z Z 2006 Acta Phys. Sin. 55 4005 (in Chinese) [王繁珍, 齐国元, 陈增强, 张宇辉, 袁著祉 2006 物理学报 55 4005]
[14]
[15]	Liu C X, Liu T, Liu L, Liu K 2004 Chaos Soliton. Fract. 22 1031
[16]	Tomasz K (translated by Shi Y) 2008 Chaos for Engineers: Theory, Application, and Control (2nd Ed.) ( Beijing: National Defense Industry Press) p62 (in Chinese) [卡毕坦尼亚克著 (施引译) 2008 面向工程的混沌学-----理论、应用及控制(第2版) (北京: 国防工业出版社) 第62页]
[17]
[18]
[19]	Zhong G Q, Tang W K S 2002 Int. J. Bifur. Chaos 12 1423
[20]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[21]

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