文档介绍：太原理工大学
硕士学位论文
一个分数阶四维动力系统的混沌研究及同步控制
姓名:潘红
申请学位级别:硕士
专业:@
指导教师:魏毅强
20100501
太原理工大学硕士研究生学位论文
一个分数阶四维动力系统的混沌研究及同步控制

摘要

分数阶混沌系统的理论及其同步研究是非线性科学的研究热点。本文
以一个四维分数阶动力系统为研究对象,采用理论分析和数值仿真相结合
的方法研究该分数阶动力系统的混沌性质及其同步控制。

混沌状态的性质定理,并通过分数阶导数的恒等形式,预估-校正算法将分
数阶系统进行离散化,给出了分数阶微分系统的数值解。
,做出系统吸引子相图和计算
Lyapunov指数,详细分析了该分数阶动力系统的混沌性质,发现了该分数
阶动力系统随系统参数和系统阶数变化而呈现混沌状态的规律。即,在参
数固定时,该分数阶动力系统均随阶数变化而分别呈现周期状态、超混状
态,为该分数阶混沌系统的应用奠定了理论基础。
,实现了不同初值的两个分数阶混沌系统
的同步控制。仿真结果表明,同步系统的同步性能很好,为该分数阶混沌
系统的应用奠定了技术基础。

关键词:混沌,分数阶,超混沌,同步控制

I
太原理工大学硕士研究生学位论文
STUDYING CHAOS AND SYNCHRONIZATION
OF A FRACTIONAL ORDERFOUR-DIMENTIONAL DYNAMIC
SYSTEM

ABSTRACT

Study of theories and applications of fractional chaotic systems is a
hot topic in the field of nonlinear science . taking a new
four-dimensional fractional order dynamic system as the model,adopting
the methods of theory analysis and numerical simulation,the chaotic
characteristic and synchronization control are studied.
First of all, On the basis of the stable theory for fractional linear
systems,it is given the theory about that the fractional order nonlinear
chaotic system is chaotic .the numerical solution of fractional differential
systems are given through the predictor-corrector algorithm with the
identity of fractional derivative
Secondly, Adopting Matlab and numerical simulation ,it give
attractors phase diagrams and calculat the Lyapunov exponent,the chaotic
characteristic of chaotic system are analyzed in detail。and
II
太原理工大学硕士研究生学位论文
the rule of appearing the chaotic states is discovered with both the
parameter and the fractional order chaotic system is periodic
and hyperchaos with the fixed system lays a theoretical
foundation for the applications of fractional order chaotic systems.
Thirdly, Synchronization control of two fractional-ord