不同类型混沌吸引子的复合

艾星星; 孙克辉; 贺少波

doi:10.7498/aps.63.040503

摘要

为了实现不同类型混沌吸引子之间的复合，采用理论分析、数值仿真和电路仿真方法，通过设计合适的切换控制器实现了不同两涡卷混沌系统之间的复合、不同多涡卷混沌系统之间的复合、两涡卷混沌系统与两翅膀混沌系统之间的复合和多涡卷混沌系统与多翅膀混沌系统之间的复合. 通过观察吸引子相图、最大Lyapunov指数和Poincaré截面，分析了复合系统的动力学行为. 设计了复合多涡卷-多翅膀吸引子的模拟电路，并对其进行了电路仿真，得到的电路仿真结果与数值仿真结果相一致. 这表明利用切换控制器实现不同类型混沌系统之间复合方法的正确性.

关键词:

Abstract

To obtain compound attractors between different chaotic systems, based on theoretical analysis, numerical simulation, and circuit simulation methods, compound attractors between different 2-scroll systems, between different multi-scroll chaotic systems, between 2-scroll system and 2-wing system and between multi-scroll system and multi-wing system, are designed via switching control. Dynamical characteristics of the system are analyzed by observing the attractor phase diagram, the largest Lyapunov exponent and the Poincaré section. A circuit for a compound multiple scroll-multiple wing chaotic attractor is designed and simulated. Numerical simulation and circuit simulation are consistent with each other. It shows that the method of obtaining compound attractors between different chaotic systems via switching control is correct.

Keywords:

作者及机构信息

1.
中南大学物理与电子学院, 长沙 410083;

2.
新疆大学物理科学与技术学院, 乌鲁木齐 830046

基金项目: 国家自然科学基金（批准号：61161006, 61073187）资助的课题.

Authors and contacts

1.
School of Physics and Electronics, Central South University, Changsha 410083, China;

2.
School of Physics Science and Technology, Xinjiang University, Urumqi 830046, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61161006, 61073187).

参考文献

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Yu S M, L J H 2012 Circuits Syst. 59 1015
[3]	Kais B, Abdessattar C, Ahmed T 2011 Chaos Solitions Fract. 44 79
[4]	L J H, Yu X H, Chen G R 2003 Circuits Syst. 50 198
[5]	Zhou X, Wang C H, Guo X R 2012 Acta Phys. Sin. 61 200506 (in Chinese) [周欣, 王春华, 郭小蓉 2012 物理学报 61 200506]
[6]	Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 物理学报 54 1500]
[7]	Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华, 禹思敏 2006 物理学报 55 5707]
[8]	Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞, 禹思敏 2009 物理学报 58 120]
[9]	Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强, 刘崇新 2007物理学报 56 1983]
[10]	Chen L, Peng H J, Wang D S 2008 Acta Phy. Sin. 57 3337 (in Chinese) [谌龙, 彭海军, 王德石 2008 物理学报 57 3337]
[11]	Bao B C, Xu Q, Xu Y M, Wang X F 2011 J. Circuits Syst. 16 69 (in Chinese) [包伯成, 徐强, 徐煜明, 汪小锋 2011 电路与系统学报 16 69]
[12]	Mustafa T, Hidayet O 2010 Expert Syst. Appl. 37 8667
[13]	Yu S M, L J H, Chen G R 2007 Phys. Lett. A 364 244
[14]	Sanchez-Lopez C 2011 Appl. Math. Comput. 217 4350
[15]	Xu F, Yu P 2010 J. Math. Anal. Appl. 362 252
[16]	Li G L, Chen X Y 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 194
[17]	Liu C X, Yi J, Xi X C, An L M, Qian Y, Fu Y Q 2012 Proc. Eng. 29 957
[18]	Zhang C X, Yu S M 2012 Int. J. Bifurcat. Chaos 22 1250120

施引文献

[1]	Lorenz E N 1963 J. Atmos. Sci. 20 130
[2]	Yu S M, L J H 2012 Circuits Syst. 59 1015
[3]	Kais B, Abdessattar C, Ahmed T 2011 Chaos Solitions Fract. 44 79
[4]	L J H, Yu X H, Chen G R 2003 Circuits Syst. 50 198
[5]	Zhou X, Wang C H, Guo X R 2012 Acta Phys. Sin. 61 200506 (in Chinese) [周欣, 王春华, 郭小蓉 2012 物理学报 61 200506]
[6]	Yu S M 2005 Acta Phys. Sin. 54 1500 (in Chinese) [禹思敏 2005 物理学报 54 1500]
[7]	Liu M H, Yu S M 2006 Acta Phys. Sin. 55 5707 (in Chinese) [刘明华, 禹思敏 2006 物理学报 55 5707]
[8]	Zhang C X, Yu S M 2009 Acta Phys. Sin. 58 120 (in Chinese) [张朝霞, 禹思敏 2009 物理学报 58 120]
[9]	Wang F Q, Liu C X 2007 Acta Phys. Sin. 56 1983 (in Chinese) [王发强, 刘崇新 2007物理学报 56 1983]
[10]	Chen L, Peng H J, Wang D S 2008 Acta Phy. Sin. 57 3337 (in Chinese) [谌龙, 彭海军, 王德石 2008 物理学报 57 3337]
[11]	Bao B C, Xu Q, Xu Y M, Wang X F 2011 J. Circuits Syst. 16 69 (in Chinese) [包伯成, 徐强, 徐煜明, 汪小锋 2011 电路与系统学报 16 69]
[12]	Mustafa T, Hidayet O 2010 Expert Syst. Appl. 37 8667
[13]	Yu S M, L J H, Chen G R 2007 Phys. Lett. A 364 244
[14]	Sanchez-Lopez C 2011 Appl. Math. Comput. 217 4350
[15]	Xu F, Yu P 2010 J. Math. Anal. Appl. 362 252
[16]	Li G L, Chen X Y 2009 Commun. Nonlinear Sci. Numer. Simulat. 14 194
[17]	Liu C X, Yi J, Xi X C, An L M, Qian Y, Fu Y Q 2012 Proc. Eng. 29 957
[18]	Zhang C X, Yu S M 2012 Int. J. Bifurcat. Chaos 22 1250120

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