JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (11): 104-112.doi: 10.6040/j.issn.1671-9352.0.2014.443

Previous Articles     Next Articles

A new four-dimensional smooth four-wing hyperchaotic system and its circuit implementation

WANG Jie-zhi1, LI Hang2, WANG Rui3, WANG Lu4, WANG Yan-chao5   

  1. 1. College of Science, Civil Aviation University of China, Tianjin 300300, China;
    2. Economics and Management College, Civil Aviation University of China, Tianjin 300300, China;
    3. College of Aeronautical Automation, Civil Aviation University of China, Tianjin 300300, China;
    4. Chief Engineer Office, Shandong Guoqiang Hardware Technology Cor. Ltd, Leling 253600, Shandong, China;
    5. Maintenance Management Department of Engineering Technology Company, China Eastern Airlines Cor. Ltd, Shanghai 200335, China
  • Received:2014-10-09 Revised:2015-02-11 Online:2015-11-20 Published:2015-12-09

PDF (PC)

761

Abstract: Using nonlinear state feedback control, a new four-dimensional smooth autonomous hyperchaotic system was constructed with large positive Lyapunov exponent. This system had larger four-wing hyperchaotic region. The stability of equilibria was discussed. The dynamic behaviors of this system were analysed through Lyapunov exponents, bifurcation diagrams and Poincaré sections. The four-wing chaotic attractor and hyperchaotic attractors were displayed by phase portraits. With various parameters, this system still underwent quasi-periodic orbits and periodic orbits. An electronic circuit is given to implement the typical hyperchaotic attractor.

Key words: Lyapunov exponent, four-wing attractor, section, circuit implementation, Poincaré, hyperchaotic system

CLC Number: 

  • O415.5
[1] RÖSSLER Otto E. An equation for hyperchaos[J]. Physics Letters A, 1979, 71(2/3):155-157.
[2] LI Yuxia, CHEN Guanrong, TANG Wallace K S. Controlling a unified chaotic system to hyperchaotic[J]. IEEE Transactions on Circuits and Systems-II, 2005, 52(4):204-207.
[3] WANG Jiezhi, CHEN Zengqiang, YUAN Zhuzhi. The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system[J]. Chinese Physics, 2006, 15(6):1216-1225.
[4] WANG Faqiang, LIU Chongxin. Hyperchaos evolved from the Liu chaotic system[J]. Chinese Physics, 2006, 15(5):963-968.
[5] WANG Jiezhi, CHEN Zengqiang, YUAN Zhuzhi. The generation and analysis of a new four-dimensional hyperchaotic system[J]. International Journal of Modern Physics C, 2007, 18(6):1013-1024.
[6] 王兴元, 王明军. 超混沌Lorenz系统[J]. 物理学报, 2007, 56(9):5136-5141. WANG Xingyuan, WANG Mingjun. Hyperchaotic Lorenz system[J]. Acta Physica Sinica, 2007, 56(9):5136-5141.
[7] CHEN Zengqiang, YANG Yong, QI Guoyuan, et al. A novel hyperchaos system only with one equilibrium[J]. Physics Letters A, 2007, 360(6):696-701.
[8] GAO Tiegang, CHEN Guanrong, CHEN Zengqiang, et al. The generation and circuit implementation of a new hyper-chaos based upon Lorenz system[J]. Physics Letters A, 2007, 361(1-2):78-86.
[9] WU Wenjuan, CHEN Zengqiang, YUAN Zhuzhi. The evolution of a novel four-dimensional autonomous system:Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos[J]. Chaos, Solitons and Fractals, 2009, 39(5):2340-2356.
[10] LIU Minghua, FENG Jiuchao, TSE Chi K. A new hyperchaotic system and its circuit implementation[J]. International Journal of Bifurcation and Chaos, 2010, 20(4):1201-1208.
[11] 张伟强,刘扬正. 统一超混沌系统的构建与电路实现[J]. 山东大学学报:理学版, 2011, 46(7):30-34. ZHANG Weiqiang, LIU Yangzheng. Generation and circuit implementation of a unified hyperchaotic system[J]. Journal of Shandong University:Natural Science, 2011, 46(7):30-34.
[12] 高智中. 一个新的四维超混沌系统及其分析[J]. 武汉大学学报:理学版, 2011, 57(3):201-204. GAO Zhizhong. A novel four-dimensional hyperchaotic system and its analysis[J]. Journal of Wuhan University:Natural Science Edition, 2011, 57(3):201-204.
[13] LI Chunlai, XIONG Jianbin, LI Wen. A new hyperchaotic system and its generalized synchronization[J]. Optik, 2014, 125:575-579.
[14] 杨敏, 俞建宁, 张建刚, 等. 一个新混沌纠缠系统的构造及动力学分析[J]. 河北师范大学学报:自然科学版, 2014, 38(3):245-249. YANG Min, YU Jianning, ZHANG Jiangang, et al. Construction and dynamical analysis of a new chaos entanglement system[J]. Journal of Hebei Normal University:Natural Science Edition, 2014, 38(3):245-249.
[15] YU Simin, MA Zaiguang, QIU Shuisheng. Generation and synchronization of n-scroll chaotic and hyperchaotic attractors in fourth-order systems[J]. Chinese Physics, 2004, 13(3):317-328.
[16] GRASSI Giuseppe, SEVERANCE Frank L, MASHEV Emil D, et al. Generation of a four-wing chaotic attractor by two weakly-coupled Lorenz systems[J]. International Journal of Bifurcation and Chaos, 2008, 18(7):2089-2094.
[17] 胡国四. 一类具有四翼吸引子的超混沌系统[J]. 物理学报, 2009, 58(6):3734-3741. HU Guosi. A family of hyperchaotic systems with four-wing attractors[J]. Acta Physica Sinica, 2009, 58(6):3734-3741.
[18] 王忠林, 邓斌, 侯承玺, 等. 四翼Liu 混沌系统的设计与电路实现[J]. 山东大学学报:理学版, 2010, 45(11):43-46. WANG Zhonglin, DENG Bin, HOU Chengxi, et al. Design and circuit realization of a four-wing Liu chaotic system[J]. Journal of Shandong University:Natural Science, 2010, 45(11):43-46.
[19] YU Simin, TANG W K S, L Jinhu, et al. Design and implementation of multi-wing butterfly chaotic attractors via Lorenz-type systems[J]. International Journal of Bifurcation and Chaos, 2010, 20(1):29-41.
[20] 刘崇新. 一个超混沌系统及其分数阶电路仿真实验[J]. 物理学报, 2007, 56(12):6865-6873. LIU Chongxin. A hyperchaotic system and its fractional order circuit simulation[J]. Acta Physica Sinica, 2007, 56(12):6865-6873.
[21] 王忠林, 姚福安, 李祥峰. 基于FPGA 的一个超混沌系统设计与电路实现[J]. 山东大学学报:理学版, 2008, 43(12):93-96. WANG Zhonglin, YAO Fuan, LI Xiangfeng. Design and realization of a hyperchaotic system based FPGA[J]. Journal of Shandong university:Natural Science, 2008, 43(12):93-96.
[22] CANG Shijian, QI Guoyuan, CHEN Zengqiang. A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system[J]. Nonlinear Dyn, 2010, 59:515-527.
[23] ZHANG Jianxiong, TANG Wansheng. A novel bounded 4D chaotic system[J]. Nonlinear Dyn, 2012, 67:2455-2465.
[24] XUE Wei, QI Guoyuan, MU Jingjing, et al. Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system[J]. Chin Phys B, 2013, 22(8):329-336.
[25] WANG Jiezhi, ZHANG Qing, CHEN Zengqiang, et al. Local bifurcation analysis and ultimate bound of a novel 4D hyper-chaotic system[J]. Nonlinear Dynamics, 2014, 78(4):2517-2531.
[26] QI Guoyuan, CHEN Guanrong, van WYK Michal Antonie, et al. A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system[J]. Chaos, Solitons and Fractals, 2008, 38(3):705-721.
[1] SONG Xing-shen, YANG Yue-xiang, JIANG Yu. Efficient multiple sets intersection using SIMD instructions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(3): 54-62.
[2] GAO Zhen-zhen, YANG Shi-lin, OBUL Abdukadir. Anick resolution and some homological properties of quantum group Uq(sl2) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(10): 17-27.
[3] ZHANG Wei-qiang, LIU Yang-zheng*. Generation and circuit implementation of a unified hyperchaotic system [J]. J4, 2011, 46(7): 30-34.
[4] WANG Zhong-lin1, DENG Bin2, HOU Cheng-xi2, YAO Fu-an2. Design and circuit realization of a four-wing Liu chaotic system [J]. J4, 2010, 45(11): 43-46.
[5] WANG Zhong-Lin, YAO Fu-An, LI Xiang-Feng. Design and realization of a hyperchaotic system based FPGA [J]. J4, 2008, 43(12): 93-96.
[6] LIU Ji-qin and HAO Xiu-mei . The dual form of the representation theorem of the both-branch fuzzy set [J]. J4, 2007, 42(5): 9-13 .
[7] LIU Ruo-Hui,LIU Bao-Cang . α-Embedding of rough both-branch fuzzy sets [J]. J4, 2007, 42(12): 77-81 .
[8] LIU Ji-qin . The dual form of representation theorem of singlebranch fuzzy set [J]. J4, 2006, 41(1): 57-61 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd