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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (4): 401-405    DOI: 10.3785/j.issn.1008-9497.2016.04.004
数学与计算机科学     
新三维非线性混沌系统的动力学特性分析
张勇1, 胡永才1, 舒永录2
1. 河南工业职业技术学院 基础教学部, 河南 南阳 473000;
2. 重庆大学 数学与统计学院, 重庆 401331
Dynamical analysis of a new 3D nonlinear chaotic system
ZHANG Yong1, HU Yongcai1, SHU Yonglu2
1. Department of Basic Teaching, Henan Polytechnic Institute, Nanyang 473000, Henan Province, China;
2. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
 全文: PDF(1200 KB)  
摘要： 基于动力系统的理论和方法，结合理论分析和Matlab仿真，利用微分方程比较定理和多元函数的Lagrange 乘数法，研究了一类新混沌系统的最终界和全局指数吸引集.对于系统的任意参数，分别得到了该混沌系统最终界和全局吸引集统一的数学表达式.最后，Matlab模拟验证了理论结果的正确性.为该系统的混沌控制、混沌同步、混沌吸引子维数的估计提供了理论依据.
关键词： 混沌系统;  混沌吸引子;  最终界;  全局吸引集;  数值仿真    
Abstract: Based on the theory and the method of dynamical systems, the authors further investigated complex dynamical behaviors of a new chaotic system by theoretical analysis and Matlab simulation combined method. The ultimate bounds and global attractive sets of the system were obtained. Then, the unified mathematical expression of the ultimate bounds and global attractive sets of the system were obtained by the comparison theorem of differential equations and Lagrange multiplier method. Finally, Matlab simulation result verified the correctness of the theoretical results. This article provides a theoretical basis for chaos control, chaos synchronization, chaos attractor dimension estimate of this system.
Key words: chaotic systems    chaotic attractor    ultimate bounds    global attractive set    Matlab simulations
收稿日期: 2015-11-15 出版日期: 2016-04-28
CLC:  O241.84  
基金资助: 国家自然科学基金资助项目（11171360）.
通讯作者: 胡永才,ORCID:http://orcid.org/0000-0003-0496-6446,E-mail:huyongcai1212@sina.com.     E-mail: huyongcai1212@sina.com
作者简介: 张勇(1981-),ORCID:http://orcid.org/0000-0001-6973-4529,男,硕士,讲师,主要从事混沌系统理论及其应用研究,E-mail:zhangyongzhang2013@163.com.
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引用本文:

张勇, 胡永才, 舒永录. 新三维非线性混沌系统的动力学特性分析[J]. 浙江大学学报（理学版）, 2016, 43(4): 401-405.

ZHANG Yong, HU Yongcai, SHU Yonglu. Dynamical analysis of a new 3D nonlinear chaotic system. Journal of ZheJIang University(Science Edition), 2016, 43(4): 401-405.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.04.004    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I4/401

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