Matlab新型分数阶混沌系统的电路仿真与设计

摘要分数阶混沌系统相比于整数阶混沌系统，它具有更加丰富的、复杂的动力学特征，且利用分数阶的积分算子更能准确描述系统的实际情况。本文主要研究了分数阶的混沌系统，首先构建了一个分数阶混沌系统，然后对其进行了动力学特征的分析，接着利用预估-校正法对这个系统进行Matlab仿真，从而得到混沌吸引子的相图。之后，基于分数阶微积分理论与波特图频域近似方法，设计出其振荡电路，再通过Multisim软件仿真该电路得到相图。从而，本文通过理论分析、数值仿真（Matlab仿真）与电路仿真（Multisim仿真）验证了系统存在混沌现象。最后，本文利用Protel DXP软件完成实际混沌电路验证算法的正确性和有效性。85038

毕业论文关键词分数阶混沌系统混沌吸引子数值仿真电路仿真

毕业设计说明书外文摘要

Title Circuit simulation and design of a new fractional order chaotic system

Abstract Compared with the integer order chaotic system, the fractional order chaotic system has more abundant and complex dynamic characteristics, and it is more accurate to describe the actual situation of the system by using the integral operator of fractional order。 The fractional order chaotic system is mainly studied in this paper。 Firstly, a fractional order chaotic system is constructed, and then the dynamic characteristics of the system are analyzed。 Secondly, the Matlab simulation of the system is carried out by the predictor corrector method, in order to obtain phase diagram of the chaotic attractor。 After that, based on the fractional order calculus theory and the Potter chart frequency domain approximation method, the oscillation circuit is designed, and the circuit is simulated by Multisim software。 Thus, the theoretical analysis, numerical simulation (Matlab simulation) and circuit simulation (Multisim simulation) verify the existence of chaos in the system。 Finally, by using Protel DXP software, the actual circuits verify that the algorithm is correct and effective。

Keywords Fractional order chaotic system Chaotic attractor numerical simulation circuit simulation

1 绪论 1

1。1 研究背景 1

2 混沌及分数阶微积分基本理论 4

2。1 混沌的定义 4

2。2 混沌运动的基本特征 6

2。3 混沌的判别方法 7

2。4 分数阶微积分 8

2。5 本章小结 10

3 新型分数阶混沌系统的电路仿真 11

3。1 系统模型 11

3。2 新型分数阶混沌系统的动力学特性 11

3。3 MATLAB数值仿真 12

3。4 电路设计与仿真分析 15

3。5 本章小结 21

4 新型分数阶混沌系统的硬件实现 22

4。1 新型分数阶混沌系统的电路改进 22

4。2 改进电路仿真 23

4。3 硬件电路的实现 25

4。4 本章小结 Matlab新型分数阶混沌系统的电路仿真与设计:http://www.youerw.com/zidonghua/lunwen_101444.html