参数未知的新超混沌Volta's系统的自适应同步

兰州理工大学学报 ›› 2020, Vol. 46 ›› Issue (3): 150-154.

参数未知的新超混沌Volta's系统的自适应同步

张志明¹, 张一帆², 李天增³

1.河南牧业经济学院软件学院,河南郑州 450046;
2.河南牧业经济学院智能制造与自动化学院, 河南郑州 450046;
3.四川理工学院数学与统计学院,四川自贡 643000

收稿日期:2018-10-23 出版日期:2020-06-28 发布日期:2020-08-19
作者简介:张志明(1980-),男,河南中牟人,硕士,讲师.
基金资助:
四川省教育厅项目(18ZA0342),河南省重大科技专项(161100510200,161100110900)

Adaptive synchronization of a new hyperchaotic Volta's system with uncertaing parameters

ZHANG Zhi-ming¹, ZHANG Yi-fan², LI Tian-zeng³

1. College of Software, Henan University of Animal Husbandry and Economy, Zhengzhou 450046, China;
2. College of Intelligent Manufacturing and Automation, Henan University of Animal Husbandry and Economy, Zhengzhou 450046, China;
3. School of Science, Sichuan University of Science and Engineering, Zigong 643000, China

Received:2018-10-23 Online:2020-06-28 Published:2020-08-19

摘要/Abstract

摘要： 在Volta's系统的基础上通过添加线性控制器得到一个新的超混沌系统.利用分统计岔图、Lyapunov指数谱和相图研究新系统随参数变化的超混沌和混沌行为,运用Lyapunov稳定定理和自适应控制理论, 实现了参数未知的两个超混沌系统的同步.计算机仿真结果验证了提出的方法的正确性和有效性.

关键词: 超混沌系统, 反馈控制, Lyapunov指数谱

Abstract: A new hyperchaotic system based on Volta's system is presented via adding linear control.The hyperchaotic behavior and chaotic behavior of this new 4D Volta's system are studied by Bifurcation diagram, Lyapunov exponents spectrum and phase diagram.The hyperchaotic behavior and chaotic behavior of this new 4D Volta's system with varying parameters are studied by Bifurcation diagram, Lyapunov exponents spectrum and phase diagram.Then, the Lyapunov stability theorem and the adaptive control theory are both employed to realize synchronization of the two hyperchaos with unknown parameters.Our simulation results have demonstrated effectiveness and validity of the proposed method.

Key words: hyperchaotic system, feedback control, Lyapunov exponents spectrum

中图分类号:

O175

张志明, 张一帆, 李天增. 参数未知的新超混沌Volta's系统的自适应同步[J]. 兰州理工大学学报, 2020, 46(3): 150-154.

ZHANG Zhi-ming, ZHANG Yi-fan, LI Tian-zeng. Adaptive synchronization of a new hyperchaotic Volta's system with uncertaing parameters[J]. Journal of Lanzhou University of Technology, 2020, 46(3): 150-154.

参考文献

[1] PODLUBNY I.Fractional differential equations [M].San Diego:Academic Press,1999.
[2] MATSUMOTO T,CHUA L,KOBAYSHI K.Laboratory experiment and numerical confirmation [J].IEEE Trans Circuits Syst,1986,33(11):1143-1147.
[3] 王划,盛潇澍,昝鹏.基于一种新的混沌系统的动态分析和图像显示 [J].电测与仪表,2017,54(3):67-71.
[4] 郑广超,刘崇新,王琰.一种具有隐藏吸引子的分数阶混沌系统的动力学分析及有限时间同步 [J].物理学报,2018 (5):43-50.
[5] JIANG P,WANG B,BU S,et al.Hyperchaotic synchronization in deterministic small-world dynamical networks [J].Int J Mod Phys B,2004,18:2674-2681.
[6] 高子林,王银河.一类不确定混沌系统的自适应模糊同步控制 [J].复杂系统与复杂性科学,2017,4:1-9.
[7] 邵克勇,韩峰,郭浩轩.一类分数阶超混沌系统的自适应有限时间控制 [J].吉林大学学报(信息科学版),2018(1):24-30.
[8] LI T,WANG Y,YANG Y.Designing synchronization schemes for fractional-order chaotic system via a single state fractional-order controller [J].Optik-International Journal for Light and Electron Optics,2014,125(22):6700-6705.
[9] WANG Y,LI T.Stability analysis of fractional-order nonlinear systems with delay [J].Mathematic Problems in Engineering,2014,125(22):6700-6705.
[10] CANNAS B,CINCOTTI S.Hyperchaotic behaviour of two bi-directionally coupled Chua's circuits [J].Int J Circuit Th Appl,2002,30(6):625-637.
[11] KAPTIANIAK T,CHUA L.Hyperchaotic attractors of unidirectionally coupled Chua's CircuitsInt [J].J Bifur Chaos,1994,4(2):477-482.
[12] WU X,GUAN Z,WU Z.Adaptive synchronization between two different hyperchaotic systems [J].Nonlinear Analysis,2008,68:1346-1351.
[13] WANG X,WANG M.A hyperchaos generated from Lorenz system [J].Physica A,2008,68(5):1346-1351.
[14] ROSSLER O.An equation for hyperchaos [J].Phys Lett A,1979,71(2):155-157.
[15] JIN Y,CHI C,AN P,et al.Controlling hyperchaos of the Rssler system [J].Int J Cont,1999,72(10):882-886.
[16] CHEN A,LU J,YU S.Generating hyperchaotic L attractor via state feedback control [J].Physica A,2006,364:103-110.
[17] LI Y,TANG W,CHEN G.Generating hyperchaos via state feedback control [J].Internat J Bifur Chaos,2005,15(10):3367-3375.
[18] ZHENG S,DONG G,BI Q.A new hyperchaotic system and its synchronization [J].Applied Mathematics and Computation,2010,215(9):3192-3200.
[19] GRASSI G,MASCOLO S.A systematic procedure for synchronizing hyperchaos via observer design [J].J Circuits Syst Comput,2002,11(1):1-16.
[20] HAO B.Elementary symbolic dynamics and chaos in dissipative systems [M].Singapore:World Scientific,1989.
[21] 张一帆,张志明,李天增.一个新的分数阶超混沌系统的同步 [J].兰州理工大学学报,2016,42(2):154-158.
[22] 张志明,张一帆,王瑜.基于分数阶控制器的分数阶混沌系统同步 [J].兰州理工大学学报,2016,42(4):158-164.