在线阅读 --自然科学版 2019年6期《一个具有四翼吸引子的超混沌系统》
一个具有四翼吸引子的超混沌系统--[在线阅读]
张莉1, 谢悦2, 安新磊2
1. 兰州工业学院 基础学科部, 甘肃 兰州 730050;
2. 兰州交通大学 数理学院, 甘肃 兰州 730070
起止页码: 490--496页
DOI: 10.13763/j.cnki.jhebnu.nse.2019.06.007
摘要
构造了一个具有四翼超混沌吸引子的非线性系统,通过对Poincaré截面、吸引子和Lyapunov指数等分析揭示新系统中超混沌吸引子的存在.根据Routh-Hurwitz准则发现,系统有1个不稳定鞍点、6个不稳定焦点和2个稳定焦点.分析了参数c变化对系统动力学的影响,数值仿真显示该系统发生了典型的倍周期分岔现象,最终通往混沌.所提出的四翼超混沌系统在保密通信和信息安全等领域有很好的应用前景.

A Hyper-chaotic System with Four-wing Attractor
ZHANG Li1, XIE Yue2, AN Xinlei2
1. Department of Basic Courses, Lanzhou Institute of Technology, Gansu Lanzhou 730050, China;
2. School of Mathematics and Physics, Lanzhou Jiaotong University, Gansu Lanzhou 730070, China
Abstract:
A nonlinear system with four-wing hyperchaotic attractors is built,and its hyperchaotic characteristics by the analysis of Poincaré sections,the power spectrum and Lyapunov exponents are verified in this paper.We have studied,the stability for equilibrium points of the system,and found that the system has an unstable saddle point,six unstable focuses and two stable focus.The impact of parameteron system dynamics is discussed,and numerical simulation results show that there is a typical double period bifurcation phenomenon,which results in chaos eventually.The proposed hyper-chaotic system with four wings has potential applications in the fields of secret communication and information safety.

收稿日期: 2019-07-21
基金项目: 甘肃省自然科学基金(17JR5RA096);兰州工业学院青年科技创新项目(17K-016)

参考文献:
[1]LORENZ E N.Deterministic Nonperiodic Flow[J].Journal of the Atmospheric Sciences,1963,20(2):130-141.
[2]CHEN Guanrong,UETA T.Yet Another Chaotic Attractor[J].International Journal of Bifurcation and Chaos,1999,9(7):1465-1466.doi:10.1142/s0218127499001024
[3]LYU Jinhu,CHEN Guanrong.A New Chaotic Attractor Coined[J].International Journal of Bifurcation and Chaos,2002,12(3):659-661.doi:10.1155/2013/980578
[4]SINGH-PIYUSH P,SINGH J P,BORAH M.On the Construction of a New Chaotic System[J].IFAC-papers Online,2016,49(1):522-525.doi:10.1016/j.ifacol.2016.03.107
[5]齐芳,张晓丹,聂少敏.一类3D四翼倍增混沌系统及Hash函数算法[J].济南大学学报,2016,30(3):195-202.doi:10.13349/j.cnki.jdxbn.2016.03.006 QI Fang,ZHANG Xiaodan,NIN Shaomin.A Class of 3D Four-wing Multiplication Chaotic System and Algorithm of Hash Functions[J].Journal of University of Jinan,2016,30(3):195-202.
[6]彭再平,王春华,林愿.一种新型的四维多翼超混沌吸引子及其在图像加密中的研究[J].物理学报,2014,63(24):240506-1.doi:10.7498/aps.63.240506 PENG Zaiping,WANG Chunhua,LIN Yuan.A Novel Four-dimensional Multi-wing Hyper-chaotic Attractor and Its Application in Image Encryption[J].Acta Physica Sinica,2014,63(24):240506-1.
[7]王繁珍,齐国元,陈增强.一个四翼混沌吸引子[J].物理学报,2007,56(6):3137-3144.doi:10.3321/j.issn.1000-3290.2007.06.019 WANG Fanzhen,QI Guoyuan,CHEN Zengqiang.On a Four-winged Chaotic Attractor[J].Acta Physica Sinica,2007,56(6):3137-3144.
[8]胡春华,王忠林,王春梅,等.可产生多翼吸引子的混沌系统及其电路实现[J].华侨大学学报,2017,38(3):300-305.doi:10.11830/issn.1000-5013.201703004 HU Chunhua,WANG Zhonglin,WANG Chunmei,et al.Construction of Chaotic System with Multi-winged Attractors and Its Circuit Implementation[J].Journal of Huaqiao University,2017,38(3):300-305.
[9]孙克辉,刘璇,朱从旭.四翼超混沌系统的动力学特性分析及其电路实现[J].电路与系统学报,2013,18(1):285-289.doi:10.1016/j.proeng.2012.01.124 SUN Kehui,LIU Xuan,ZHU Congxu.Dynamics of a Four-wing Hyperchaotic System and Its Circuit Implementation[J].Journal of Circuits and Systems,2013,18(1):285-289.