Horseshoe and entropy in a fractional-order unified system

被引：0
|
作者：
李清都 [1 ,2 ]
陈述 [1 ]
周平 [2 ]
机构：
[1] Key Laboratory of Networked Control and Intelligent Instrument of Ministry of Education,Chongqing University of Posts and Telecommunications
[2] Institute for Nonlinear Systems,Chongqing University of Posts and Telecommunications
来源：
Chinese Physics B | 2011年 / 20卷 / 01期
基金：
中国国家自然科学基金;
关键词：
chaos; topological horseshoe; fractional-order system; generalised Lorenz system;
D O I：
暂无
中图分类号：
O415.5 [混沌理论];
学科分类号：
070201 ;
摘要：
This paper studies chaotic dynamics in a fractional-order unified system by means of topological horseshoe theory and numerical computation.First it finds four quadrilaterals in a carefully-chosen Poincar’e section,then shows that the corresponding map is semiconjugate to a shift map with four symbols.By estimating the topological entropy of the map and the original time-continuous system,it provides a computer assisted verification on existence of chaos in this system,which is much more convincible than the common method of Lyapunov exponents.This new method can potentially be used in rigorous studies of chaos in such a kind of system.This paper may be a start for proving a given fractional-order differential equation to be chaotic.
引用
收藏
页码：179 / 184
页数：6
相关论文
共 50 条
  • [21] Dynamics of a fractional-order simplified unified system based on the Adomian decomposition method
    Yixin Xu
    Kehui Sun
    Shaobo He
    Limin Zhang
    The European Physical Journal Plus, 131
  • [22] Dynamics of a fractional-order simplified unified system based on the Adomian decomposition method
    Xu, Yixin
    Sun, Kehui
    He, Shaobo
    Zhang, Limin
    EUROPEAN PHYSICAL JOURNAL PLUS, 2016, 131 (06):
  • [23] A unified framework of fault detection and diagnosis based on fractional-order chaos system
    Huang, Pengfei
    Chen, Xiaolong
    Chai, Yi
    Ma, Le
    AEROSPACE SCIENCE AND TECHNOLOGY, 2022, 130
  • [24] The fractional-order unified chaotic system: A general cascade synchronization method and application
    An, Hongli
    Feng, Dali
    Sun, Li
    Zhu, Haixing
    AIMS MATHEMATICS, 2020, 5 (05): : 4345 - 4356
  • [25] A Unified FPGA Realization for Fractional-Order Integrator and Differentiator
    Monir, Mohamed S.
    Sayed, Wafaa S.
    Madian, Ahmed H.
    Radwan, Ahmed G.
    Said, Lobna A.
    ELECTRONICS, 2022, 11 (13)
  • [26] Fractional-order Iterative Learning Control and Identification for Fractional-order Hammerstein System
    Li, Yan
    Zhai, Lun
    Chen, YangQuan
    Ahn, Hyo-Sung
    2014 11TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION (WCICA), 2014, : 840 - 845
  • [27] Fractional-Order Adaptive Backstepping Control of a Noncommensurate Fractional-Order Ferroresonance System
    Wang, Yan
    Liu, Ling
    Liu, Chongxin
    Zhu, Ziwei
    Sun, Zhenquan
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2018, 2018
  • [28] Fractional symbolic network entropy analysis for the fractional-order chaotic systems
    He, Shaobo
    Sun, Kehui
    Wu, Xianming
    PHYSICA SCRIPTA, 2020, 95 (03)
  • [29] Numerical Analysis, Circuit Simulation, and Control Synchronization of Fractional-Order Unified Chaotic System
    Li, Guohui
    Zhang, Xiangyu
    Yang, Hong
    MATHEMATICS, 2019, 7 (11)
  • [30] Fractional-order PD control at Hopf bifurcations in a fractional-order congestion control system
    Yuhong Tang
    Min Xiao
    Guoping Jiang
    Jinxing Lin
    Jinde Cao
    Wei Xing Zheng
    Nonlinear Dynamics, 2017, 90 : 2185 - 2198
12345