[1]颜闽秀,徐辉.四翼混沌系统及其Hopf分岔控制[J].深圳大学学报理工版,2021,38(2):180-187.[doi:10.3724/SP.J.1249.2021.02180]
　YAN Minxiu,and XU Hui.Four-wing chaotic system and its Hopf bifurcation control[J].Journal of Shenzhen University Science and Engineering,2021,38(2):180-187.[doi:10.3724/SP.J.1249.2021.02180]
点击复制

四翼混沌系统及其Hopf分岔控制()
分享到：

《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第38卷
期数:
2021年第2期
页码:
180-187
栏目:
电子与信息科学
出版日期:
2021-03-12

文章信息/Info

Title:
Four-wing chaotic system and its Hopf bifurcation control
文章编号:
202102010
作者:
颜闽秀1; 2; 徐辉1
1）沈阳化工大学信息工程学院，辽宁沈阳 110142
2）工业环境-资源协同控制与优化技术辽宁省高校重点实验室，沈阳化工大学，辽宁沈阳 110142
Author(s):
YAN Minxiu1;  2 and XU Hui1
1) College of Information Engineering, Shenyang University of Chemical Technology, Shenyang 110142, Liaoning Province, P.R.China
2) Key Laboratory for Industrial Environment-Resources Cooperative Control and Optimization Technology, Shenyang University of Chemical Technology, Shenyang 110142, Liaoning Province, P.R.China
关键词:
系统学; 四翼混沌系统; Hopf分岔; 分岔控制; 极限环; 非线性系统; 保密通信
Keywords:
systematics;  four-wing chaotic system;  Hopf bifurcation;  bifurcation control;  limit cycle;  nonlinear system;  secure communication
分类号:
TP273
DOI:
10.3724/SP.J.1249.2021.02180
文献标志码:
A
摘要:
为满足Hopf分岔控制的实际需要和通信保密对复杂混沌系统的需求，设计一个四翼混沌吸引子和基于washout滤波器的分岔控制器．基于Lorenz系统构建新的四翼系统，通过分岔图、李雅普诺夫指数和吸引子仿真分析系统的动力学演化，确定其混沌特性．基于高维Hopf分岔理论分析系统Hopf分岔的存在性，设计了一个基于washout滤波器，由线性项和非线性项组成的Hopf分岔控制器．该控制器在不改变系统平衡点的情况下，可实现系统在预期位置产生Hopf分岔，完成对极限环幅值和稳定性的控制．仿真结果表明，极限环幅值和分岔参数的临界值是可以控制的，验证了控制器的合理性和有效性．该研究拓展了混沌系统Hopf分岔控制的多样性，在通信和图像加密领域有潜在的应用．
Abstract:
In order to meet the practical needs of Hopf bifurcation control and communication security, we propose a four-wing chaotic attractor and a bifurcation controller based on washout filter. We analyze the dynamic evolution of system by means of bifurcation diagram, Lyapunov exponent and attractor simulation to determine its chaotic characteristics. Based on the high-dimensional bifurcation theory, we discuss the existence of Hopf bifurcation, and design a Hopf bifurcation controller based on washout filter, which is composed of linear and nonlinear terms. Without changing the equilibrium point of system, the controller can generate the Hopf bifurcation of system at the expected position, and realize the control of amplitude and stability of the limit cycle. The simulation results show that the amplitude of the limit cycle and the critical value of bifurcation parameters can be controlled, which verifies the rationality and effectiveness of the controller. This study expands the diversity of Hopf bifurcation control in chaotic system and has potential applications in communication and image encryption.

参考文献/References:

［1］ CHEN Ping, YU Simin, ZHANG Xiaoyang, et al. ARM-embedded implementation of a video chaotic secure communication via WAN remote transmission with desirable security and frame rate［J］. Nonlinear Dynamics, 2016, 86(2): 725-740.
［2］ GAN Qiuye, YU Simin, LI Chengqing, et al. Design and ARM-embedded implementation of a chaotic map-based multicast scheme for multiuser speech wireless communication［J］. International Journal of Circuit Theory and Applications, 2017, 45(11): 1849-1872.
［3］ LORENZ E N. Deterministic non-periodic flow［J］. Journal of the Atmospheric Sciences, 1963, 20(2): 130-141.
［4］ 庄志本，李军，刘静漪，等．基于新的五维多环多翼超混沌系统的图像加密算法［J］．物理学报，2020，69(4)：50-63．
ZHUANG Zhiben, LI Jun, LIU Jingyi, et al. Image encryption algorithm based on new five-dimensional multiring and multi-wing hyperchaotic system［J］. Acta Physica Sinica, 2020, 69(4): 50-63.(in Chinese)
［5］ 贾美美，蒋浩刚，李文静．新Chua多涡卷混沌吸引子的产生及应用［J］．物理学报，2019，68(13)：61-73．
JIA Meimei, JIANG Haogang, LI Wenjing. Generation and application of novel Chua multi-scroll chaotic attractors［J］. Acta Physica Sinica, 2019, 68(13): 61-73.(in Chinese)
［6］ HU Xiaoyu, LIU Chongxin, LIU Ling, et al. Chaotic dynamics in a neural network under electromagnetic radiation［J］. Nonlinear Dynamics, 2018, 91(3): 1541-1554.
［7］ BAO Bocheng, LIU Zhong, XU Jianping. New chaotic system and its hyper chaos generation［J］. Journal of Systems Engineering and Electronics, 2009, 20(6): 1179-1187.
［8］ NI Junkang, LIU Ling, LIU Chongxin, et al. Fractional order fixed-time nonsingular terminal sliding mode synchronization and control of fractional order chaotic systems［J］. Nonlinear Dynamics, 2017, 89(3): 2065-2083.
［9］ KAI G, ZHANG W, JIN Z, et al. Hopf bifurcation and dynamic analysis of an improved financial system with two delays［J］. Complexity, 2020, 2020(1): 1-13.
［10］ DIJKSTRA H A. Numerical bifurcation methods applied to climate models: analysis beyond simulation［J］. Nonlinear Processes in Geophysics, 2019, 26(4): 359-369.
［11］ 史昭娣，张靠社，黄越辉，等．基于Hopf分岔的风电集群系统电压稳定分析［J］．电力系统保护与控制，2017，45(14)：9-16．
SHI Zhaodi, ZHANG Kaoshe, HUANG Yuehui, et al. Analysis of voltage stability in wind power cluster system based on Hopf bifurcation［J］. Power System Protection and Control, 2017, 45(14): 9-16.(in Chinese)
［12］ KANG Wang, KRENER A J. Extended quadratic controller normal form and dynamic state feedback linearization of nonlinear systems［J］. SIAM Journal on Control and Optimization, 1992, 30(6): 1319-1337.
［13］ 刘素华，唐驾时．Langford系统Hopf分叉的线性反馈控制［J］．物理学报，2007，56(6)：120-126．
LIU Suhua, TANG Jiashi. Linear feedback control of Hopf bifurcation in Langford system［J］. Acta Physica Sinica, 2007, 56(6): 120-126.(in Chinese)
［14］ YU P, CHEN Guanrong. Hopf bifurcation control using nonlinear feedback with polynomial functions［J］. International Journal of Bifurcation and Chaos, 2004, 14(5): 1683-1704.
［15］ CHENG Zhunshui. Anti-control of Hopf bifurcation for Chen’s system through washout filters［J］. Neurocomputing, 2010, 73(16): 3139-3146.
［16］ 毛北行，王战伟．一类分数阶复杂网络系统的有限时间同步控制［J］．深圳大学学报理工版，2016，33(1)：96-101．
MAO Beixing, WANG Zhanwei. Finite-time synchronization control of a class of fractional-order complex network systems［J］. Journal of Shenzhen University Science and Engineering, 2016, 33(1): 96-101.(in Chinese)
［17］ CHEN Guanrong, LI Changpin. A note on bifurcation control［J］. International Journal of Bifurcation and Chaos, 2003, 13(3): 667-669.
［18］ CHEN Guanrong, HILL D J, YU Xinghuo. Bifurcation control: theory and applications［M］. New York, USA: Springer Science and Business Media, 2003: 1-26.
［19］ CAI P, YUAN Z Z. Hopf bifurcation and chaos control in a new chaotic system via hybrid control strategy［J］. Chinese Journal of Physics, 2017, 55(1): 64-70.
［20］ ZHANG Liang, TANG Jiashi, HAN Qin. Hopf bifurcation control of a Pan-like chaotic system［J］. Chinese Physics B, 2018, 27(9): 094702.
［21］ 张良．一个五维超混沌系统Hopf分岔控制［J］．工程数学学报，2019，36(3)：322-332．
ZHANG Liang. Hopf bifurcation control of a five-dimensional hyperchaotic system［J］. Chinese Journal of Engineering Mathematics , 2019,36(3): 322-332.(in Chinese)
［22］ ESHAGHI S, GHAZIANI R K, ANSARI A. Hopf bifurcation, chaos control and synchronization of a chaotic fractional-order system with chaos entanglement function［J］. Mathematics and Computers in Simulation, 2020, 172: 321-340.
［23］ WOLF A, SWIFT J B, SWINNEY H L, et al. Determining Lyapunov exponents from a time series［J］. Physica D: Nonlinear Phenomena, 1985, 16(3): 285-317.
［24］ MARSDEN J E, MCCRACKEN M. The Hopf bifurcation and its applications［M］. New York, USA: Springer Science and Business Media, 2012: 63-85.

相似文献/References:

[1]丰建文,何玲,吴耿,等.统一混沌系统的修改模型及同步设计[J].深圳大学学报理工版,2010,27(1):37.
　FENG Jian-wen,HE Ling,WU Geng,et al.Modified model of unified chaotic system and the design of synchronization[J].Journal of Shenzhen University Science and Engineering,2010,27(2):37.
[2]潘运亮,杜军.参数不确定混沌系统的动态面输出调节方法[J].深圳大学学报理工版,2014,31(3):307.[doi:10.3724/SP.J.1249.2014.03307]
　Pan Yunliang and Du Jun.Dynamic surface output regulation method for chaotic systems with adaptive internal model[J].Journal of Shenzhen University Science and Engineering,2014,31(2):307.[doi:10.3724/SP.J.1249.2014.03307]

备注/Memo

备注/Memo:
Received：2020-05-20；Accepted：2020-07-20
Foundation：China-Macedonia Intergovernmental Scientific and Technological Cooperation Project (［2017］25:5-5)
Corresponding author：Associate professor YAN Minxiu. E-mail: yanminxiu@syuct.edu.cn
Citation：YAN Minxiu, XU Hui. Four-wing chaotic system and its Hopf bifurcation control［J］. Journal of Shenzhen University Science and Engineering, 2021, 38(2): 180-187.（in Chinese）
基金项目：国家科技部中国-马其顿政府间科技合作资助项目（国科外［2017］25: 5-5）
作者简介：颜闽秀(1972—)，沈阳化工大学副教授、博士．研究方向：复杂系统控制和混沌理论．E-mail: yanminxiu@syuct.edu.cn
引文：颜闽秀，徐辉．四翼混沌系统及其Hopf分岔控制［J］. 深圳大学学报理工版，2021，38(2)：180-187.
更新日期/Last Update: 2021-03-30