Journal of Guangxi Normal University(Natural Science Edition) ›› 2021, Vol. 39 ›› Issue (5): 173-181.doi: 10.16088/j.issn.1001-6600.2020121402

Previous Articles     Next Articles

Research on Complex Dynamics of a New Four-dimensional Hyperchaotic System with Finite and Infinite Isolated Singularities

RUAN Wenjing, YANG Qigui*   

  1. School of Mathematics, South China University of Technology, Guangzhou Guangdong 510640, China
  • Received:2020-12-14 Revised:2021-02-03 Online:2021-09-25 Published:2021-10-19

PDF (PC)

176

Abstract: Based on the Sprott A chaotic system, by designing a feedback controller, this paper proposes a new four-dimensional autonomous hyperchaotic system with an infinite number of isolated singularities and only two symmetrical singularities. The stability of the non-hyperbolic singularities of this type of new system is discussed by using the central manifold theory, and the Hopf bifurcation is strictly proved. Furthermore, by using numerical methods such as Lyapunov exponential spectrum, bifurcation graph and Poincaré mapping, the existence of periodic attractors, chaotic attractors and hyperchaotic attractors of the new system is obtained.

Key words: hyperchaos, attractor, Hopf bifurcation, complex dynamics, stability

CLC Number: 

  • O415.5
[1] LORENZ E N. Deterministic non-periodic flow[J]. Journal of the Atmospheric Sciences, 1963, 20(2): 130-141.
[2] RÖSSLER O E. An equation for hyperchaos[J]. Physics Letters A, 1979, 71(2/3): 155-157.
[3] MATSUMOTO T, CHUA L O, KOBAYASHI K. Hyperchaos: Laboralory experiment and numerical confirmation[J]. IEEE Transaction on Circuits and Systems, 1986, 33(11): 1143-1147.
[4] SU Q, WANG C, CHEN H, et al. A new method for generating chaotic system with arbitrary shaped distributed attractors[J]. Chaos, 2018, 28(7): 073106.
[5] 张锦炎, 冯贝叶.常微分方几何理论与分支问题[M].北京: 北京大学出版社,2000: 329-378.
[6] 张芷芬, 丁同仁,黄文灶,等. 微分方程定性理论[M]. 北京: 科学出版社, 1997: 435-436.
[7] YANG T, YANG Q G. A 3D autonomous system with infinitely many chaotic attractors[J]. International Journal of Bifurcation and Chaos, 2019, 29(12): 1950166.
[8] YANG Q G, ZHANG K M, CHEN G R. Hyperchaotic attractors from a linearly controlled Lorenz system[J]. Nonlinear Analysis: Real World Applications, 2008, 10(3): 1601-1617.
[9] CHEN Y M, YANG Q G. Dynamics of a hyperchaotic Lorenz-type system[J]. Nonlinear Dynamic, 2014, 77: 569-581.
[10] YANG Q G, LIU Y J. A hyperchaotic system from a chaotic system with one saddle and two stable node-foci[J]. Journal of Mathematical Analysis and Applications, 2009, 360(1): 293-306.
[11] CHEN Y M, YANG Q G. A new Lorenz-type hyperchaotic system with a curve of equilibria[J]. Mathematics and Computers in Simulation, 2015, 112: 40-55.
[12] 张艳红.具有无穷多孤立奇点或无奇点的新四维超混沌系统的动力学研究[D].广州:华南理工大学, 2017.
[13] SPROTT J C. Some simple chaotic flows[J]. Physical Review E, 1994, 50(2): 647-650.
[14] YANG Q G, QIAO X M. Constructing a new 3D chaotic system with any number of equilibria[J]. Internatioanal Journal of Bifurcation and Chaos, 2019, 29(5): 1950060.
[15] WIGGINS S. Introduction to applied nonlinear dynamical system and chaos[M]. New York: Springer, 2003: 608-615.
[16] HASSARD B, KAZARINOFF N, WAN Y. Theory and application of Hopf bifurcation[M]. Cambridge: Cambridge University Press, 1981: 14-70.
[1] CHEN Dong, HU Kui. Cover Gorenstein AC-flat Dimensions [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(6): 51-55.
[2] ZHENG Tao, ZHOU Xinran, ZHANG Long. Global Asymptotic Stability of Predator-Competition-Cooperative Hybrid Population Models of Three Species [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(5): 64-70.
[3] WANG Junjie, WEN Xueyan, XU Kesheng, YU Ming. An Improved Stack Algorithm Based on Local Sensitive Hash [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(4): 21-31.
[4] CHEN Xiong, ZHU Yu, FENG Ke, YU Tongwei. Identity Authentication of Power System Safetyand Stability Control Terminals Based on Blockchain [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(2): 8-18.
[5] ZHANG Jie, LI Xiaojun. Existence of Uniform Random Attractor for NonautonomousStochastic Reaction-diffusion Equations on Unbounded Domains [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(2): 134-143.
[6] SHE Lianbing, GAO Yunlong. Backward-compact Dynamics for Non-autonomous Navier-Stokes Equations on Unbounded Domains [J]. Journal of Guangxi Normal University(Natural Science Edition), 2020, 38(1): 41-46.
[7] LUO Lan, ZHOU Nan, SI Jie. New Delay Partition Method for Robust Stability of Uncertain Cellular Neural Networks with Time-Varying Delays [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(4): 45-52.
[8] HONG Lingling, YANG Qigui. Research on Complex Dynamics of a New 4D Hyperchaotic System [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(3): 96-105.
[9] WU Juan, ZHU Hongyang, MEI Ping, CHEN Wu, LI Zhongbao. Polymethyl Methacrylate Modified Nano-Silica and Its Stabilizing Effect on Pickering Emulsion [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(3): 120-131.
[10] CHEN Siyu, ZOU Yanli, ZHOU Jian, TAN Huazhen. Study on the Power Allocation of Power Generators and Unbalanced Development of Loadson Power Grids [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(2): 52-59.
[11] HAN Huiqing, CAI Guangpeng, YIN Changying, MA Geng, ZHANG Yingjia, LU Yi. Analysis of Landscape Stability in Middle and Upper Reaches of the Wujiang River in 2000 and 2015 [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(1): 197-204.
[12] MIAO Xinyan, ZHANG Long, LUO Yantao, PAN Lijun. Study on a Class of Alternative Competition-Cooperation Hybrid Population Model [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(3): 25-31.
[13] MEI Chuncao， WEI Duqu*， LUO Xiaoshu. Stability Analysis of Inductive Load of Distributed Generation System [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(2): 50-55.
[14] FENG Jinming,LI Zunxian. Stability Analysis of a Class of Epidemic Model with Diffusion [J]. Journal of Guangxi Normal University(Natural Science Edition), 2018, 36(2): 63-68.
[15] ZHANG Xueliang,TAN Huili, BAI Kezhao, TANG Guoning,DENG Minyi. A Cellular Automaton Model Connected to the ConductionRestitution Property of Cardiac Cells [J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(4): 1-9.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] LI Yuhui, ZHOU Qihai, HUANG Zhonghao. Ranging Behavior and Habitat Utilization of Assamese Macaque (Macacaassamensis) during Rainy Season in Nonggang Nature Reserve, Guangxi, China[J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(4): 114 -121 .
[2] HUANG Li, ZOU Yanli, WANG Yi, LI Ke. A Comparative Study on Three Types of Distributed PowerPlant Connection Strategies[J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(3): 30 -36 .
[3] TANG Dandan, MA Jiangming, LI Haixia. Flora of Vascular Plant in Fengshui Woods on Karst Hills of Guilin[J]. Journal of Guangxi Normal University(Natural Science Edition), 2017, 35(3): 126 -132 .
[4] SHANG Jing, NI Qing-ling, GUI Liu-cheng, WANG Xiu-jian, HUANG Ting-hong, MA Kai, ZENG Jian-qiang. Synthesis of Crystal Structure of ｛HgBr2[μ2-Cu(C26H22O2N4)]｝n[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(2): 61 -64 .
[5] LIU Xi-liang, BIN Shi-yu, WANG Kai-zhuo, CHEN Dun-xue, CHENG Jia, ZHANG Jian-she, CHU Wu-ying. Artificial Propagation and Embryonic Development Observation of Mandarin Fish[J]. Journal of Guangxi Normal University(Natural Science Edition), 2013, 31(2): 100 -106 .
[6] YANG Li, KONG Ling-jiang. Capillary Force between Microparticles[J]. Journal of Guangxi Normal University(Natural Science Edition), 2012, 30(1): 1 -4 .
[7] LI Zhaomei, LI Wenlin, MENG Anxin, ZHAO Zhenchi, QIN Yongfu, LAN Haihui, LU Huijin, CHEN Lisha, LIANG Weigang, SHEN Hongtao. Study of 14C-AMS in Dating of the Ancient Painting[J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(2): 38 -43 .
[8] LIU Weiming, CHEN Gangmei, LIN Guanrong, LI Jingning. Coordination Control Method for Toll Station of Freeway and Adjacent Intersection[J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(4): 16 -26 .
[9] ZOU Yanli, WANG Yang, LIU Shusheng, YAO Fei. Study of Cascading Failure in the Grid under the Capacity Load Model with Neighbors Degree Information[J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(4): 27 -36 .
[10] ZHONG Xianggui, SUN Yue, WU Xianghua. Nearly CAP*-Subgroups and p-Supersolvability of Finite Groups[J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(4): 74 -78 .
Copyright © Journal of Guangxi Normal University(Natural Science Edition), All Rights Reserved.
Tel: 0773-5857325　E-mail: gxsdzkb@mailbox.gxnu.edu.cn
Powered by Beijing Magtech Co. Ltd