新分数阶超混沌系统的研究与控制及其电路实现

黄丽莲; 辛方; 王霖郁

doi:10.7498/aps.60.010505

摘要

为了提高混沌信号的复杂性,提出了一个新的分数阶四维超混沌系统,并对该系统的混沌动力学特性进行详细的理论分析和数值仿真,Maltab仿真证实了该分数阶超混沌系统存在混沌的最小阶数为3.2阶.同时运用Multisim软件对该系统进行电路实验仿真验证.最后设计了简单有效的线性反馈控制器,并进行电路实现,仿真结果证明了控制器是有效的.

关键词:

In order to improve the complexity of chaotic signals, a new fractional-order four-dimensional hyperchaotic system is presented. Some dynamical properties of the system are investigated. The circuit implementation of this new system is simulated using Multisim. The results prove that chaos actually exists in the system with order as low as 3.2. A simple linear feedback controller is designed, and the simulation results are presented to demonstrate the effectiveness of the method.

Keywords:

作者及机构信息

1.
哈尔滨工程大学信息与通信工程学院,哈尔滨 150001

基金项目: 国家自然科学基金(批准号:F010303)和中央高校基本科研业务费专项资金资助的课题.

Authors and contacts

1.
College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China

参考文献

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[2]	Lu J G 2006 Phys. Lett. A 354 305
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[4]	Li G L, Chen X Y 2010 Chin. Phys. B 19 030507
[5]	Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524(in Chinese) [许喆、刘崇新、杨韬 2010 物理学报 59 1524]
[6]	Liu C X 2007 Chaos, Solitons and Fractals 4 25
[7]	Gao T G, Chen G R, Chen Z Q 2007 Phys. lett. A 361 78
[8]	Wei W, Li D H, Wang J 2010 Chin. Phys. B 19 040507
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[13]	Zhang Q J, Lu J A 2008 Chin. Phys. B 17 492
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[18]	Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[19]	Liu C X, Liu L 2009 Chin. Phys. B 18 2188
[20]	Li C B, Chen S, Zhu H Q 2009 Acta Phys. Sin. 58 2255(in Chinese) [李春彪、陈谡、朱焕强 2009 物理学报 58 2255]
[21]	Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 4402(in Chinese) [胡建兵、韩焱、赵灵冬 2009 物理学报 58 4402]
[22]	Mohammad S T, Mohammad H 2007 Phys. Lett. A 367 102
[23]	Zhou P, Cheng X F, Zhang N Y 2008 Chin. Phys. B 17 3252
[24]	Li C P, Peng G J 2004 Chaos, Soliton and Fractals 22 443
[25]	Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416(in Chinese) [陈向荣、刘崇新、王发强、李永勋 2008 物理学报 57 1416]
[26]	Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456(in Chinese) [闵富红、余杨、葛曹君 2009 物理学报 58 1456]
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[29]	Matignon D 1996 IMACS, IEEE-SMC, Lille, France 963
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施引文献

[1]	Zhang R X, Yang S P 2009 Acta Phys. Sin. 58 2957(in Chinese) [张若洵、杨世平 2009 物理学报 58 2957]
[2]	Lu J G 2006 Phys. Lett. A 354 305
[3]	Zhou P, Cheng X F, Zhang N Y 2008 Acta Phys. Sin. 57 5407(in Chinese) [周平、程雪峰、张年英 2008 物理学报 59 5407]
[4]	Li G L, Chen X Y 2010 Chin. Phys. B 19 030507
[5]	Xu Z, Liu C X, Yang T 2010 Acta Phys. Sin. 59 1524(in Chinese) [许喆、刘崇新、杨韬 2010 物理学报 59 1524]
[6]	Liu C X 2007 Chaos, Solitons and Fractals 4 25
[7]	Gao T G, Chen G R, Chen Z Q 2007 Phys. lett. A 361 78
[8]	Wei W, Li D H, Wang J 2010 Chin. Phys. B 19 040507
[9]	Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549(in Chinese) [张若洵、杨世平、刘永利 2010 物理学报 59 1549]
[10]	Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305(in Chinese) [赵灵冬、胡建兵、刘旭辉 2010 物理学报 59 2305]
[11]	Liu C X 2007 Acta Phys. Sin. 56 6865(in Chinese) [刘崇新 2007 物理学报 56 6865]
[12]	Xiao Y Z, Xu W, Li X C, Tang S F 2008 Chin. Phys. B 17 80
[13]	Zhang Q J, Lu J A 2008 Chin. Phys. B 17 492
[14]	Hu J, Zhang Q J 2008 Chin. Phys. B 17 503
[15]	Zhang X F, Fan J L 2010 Acta Phys. Sin. 59 2298(in Chinese) [张雪锋、范九伦 2010 物理学报 59 2298]
[16]	Zhang L P, Jiang H B, Bi Q S 2010 Chin. Phys. B 19 010507
[17]	Jia H Y, Chen Z Q, Yuan Z Z 2009 Acta Phys. Sin. 58 4469(in Chinese) [贾红艳、陈增强、袁著祉 2009 物理学报 58 4469]
[18]	Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[19]	Liu C X, Liu L 2009 Chin. Phys. B 18 2188
[20]	Li C B, Chen S, Zhu H Q 2009 Acta Phys. Sin. 58 2255(in Chinese) [李春彪、陈谡、朱焕强 2009 物理学报 58 2255]
[21]	Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 4402(in Chinese) [胡建兵、韩焱、赵灵冬 2009 物理学报 58 4402]
[22]	Mohammad S T, Mohammad H 2007 Phys. Lett. A 367 102
[23]	Zhou P, Cheng X F, Zhang N Y 2008 Chin. Phys. B 17 3252
[24]	Li C P, Peng G J 2004 Chaos, Soliton and Fractals 22 443
[25]	Chen X R, Liu C X, Wang F Q, Li Y X 2008 Acta Phys. Sin. 57 1416(in Chinese) [陈向荣、刘崇新、王发强、李永勋 2008 物理学报 57 1416]
[26]	Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456(in Chinese) [闵富红、余杨、葛曹君 2009 物理学报 58 1456]
[27]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press) p4
[28]	Ahmad W M, Sprott J C 2003 Chaos, Solitons and Fractals 16 339
[29]	Matignon D 1996 IMACS, IEEE-SMC, Lille, France 963
[30]	Ahmed E, El2Sayed A M A, Elsaka H A A 2007 J. Math. Anal. Appl. 325 542

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