四维超Jerk系统的分岔特性及同步控制研究  

BIFURCATION AND SYNCHRONIZATION CONTROL OF A FOUR-DIMENSION HYPERJERK SYSTEM

作　　者：姜丽爽 李静[1] 张伟[2] Jiang Lishuang;Li Jing;Zhang Wei(Faculty of Science,Beijing University of Technology,Beijing 100124,China;Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学理学部,北京100124 [2]北京工业大学材料与制造学部,北京100124

出　　处：《动力学与控制学报》2021年第6期1-7,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11772007,11832002,11290152);北京市自然科学基金资助项目(1172002,Z180005)。

摘　　要：研究具有双翼混沌吸引子的四维超Jerk系统的分岔特性和混沌路径,并设计有效的自适应反馈控制器实现该系统的全局指数同步.通过相图、Poincaré映射图、分岔图和Lyapunov指数谱等揭示系统的混沌特性,并得到系统进入混沌的主要路径是逆倍周期分岔和大幅度的周期振荡.将高维分岔理论和扰动方法应用于该系统的动力学分析中,建立分岔点处参数之间的精确关系,进一步得出产生的周期轨道的稳定性及其近似解表达式.基于自适应同步理论,提出一种实现混沌系统完全同步的方案.数值模拟结果表明所提出机制的可行性和有效性.本文可为此类系统在混沌加密领域内的实际应用提供理论参考.The aim of this paper is to investigate bifurcation and chaos routes of a four-dimension hyperjerk system with double-scroll attractors,and to design an adaptive feedback controller to realize global exponential synchronization.The chaotic characteristics are revealed via phase diagram,Poincarémap,bifurcation diagram and Lyapunov exponents spectrum.It is concluded that the system achieves chaotic state through inverse period-doubling bifurcations and large amplitude periodic oscillations.Based on bifurcation theory and perturbation method,the exact relationship between the parameters at the bifurcation point is established.We further analyze stabilities of bifurcated periodic orbits and their ap⁃proximate solutions.By using a adaptive synchronization technique,a scheme to realize complete synchronization of cha⁃otic systems is proposed.Numerical simulations demonstrate that the proposed mechanism is feasible and effective.This work can provide a theoretical reference for practical applications of such system in the field of chaotic encryption.

关 键 词：超Jerk系统 奇异吸引子 分岔 周期轨道 同步控制 

分 类 号：O415.5[理学—理论物理] O231[理学—物理]