变型蔡氏混沌电路的实现_孙福艳

第25卷第2期Vol 125, No 12

西华大学学报#自然科学版Journal of Xihua U niversity #Natural Science

2006年3月M ar 12006

文章编号:1673-159X(2006) 02-0048-03

变型蔡氏混沌电路的实现

孙福艳1, 魏金成1, 王磊1, 吕宗旺2

(1. 西华大学电气信息学院, 四川成都610039; 2. 德昌电机(深圳) 有限公司, 广东深圳518125)

摘要:提出了一个新的非线性动力学系统模型, 并对其进行了理论分析、仿真和硬件电路的实现。结果证明这种变型蔡氏电路为混沌通信和混沌现象的研究提供了一种新的混沌发生器。

关键词:混沌; 混沌通信; 非线性器件; 混沌发生器; 非线形二极管中图分类号:T N 918

文献标识码:A

目前对于混沌通信的研究逐步深入, 已经有许多基于混沌同步的保密通信方法。然而目前能够用于混沌通信的混沌发生器还很少, 在一定程度上阻碍了混沌通信的实用化进程, 因而设计出性能好的混沌发生器对混沌和混沌通信的研究来说具有很大的参考价值。在混沌和混沌通信研究中, 最常用的是蔡氏双涡旋混沌电路, 其模型可描述为一个三阶非线性自治动力学系统。蔡氏电路只采用了一个非线性器件, 即一个三段线性的负阻, 并且蔡氏电路从整体结构来看是最简单的混沌发生器。此混沌发生器的动力学系统数学模型如下:

=y -py 2d S =-x +qy -r z d S =s(y -z ) d S

式中, p 、r 、s 为参数, 若p 、r 、s 一定, 随着q 的变化, 最终导致混沌吸引子的出现。

若保持蔡氏双涡旋混沌吸引子数学模型中的f (x ) 和a 、b 参数不变, 增加一个非线性函数g (y ) c , g (y ) c 是一个两段线形函数, 变型电路的原理如图1所示:

图1 变型蔡氏电路原理图

由变型蔡氏电路原理图可得如下的状态方程:d i L

=-U C 1d t d U C 1C 1=-(U C 1-U C 2) -f (x )

d t R V L C 2

d U C 2=(U C 1-U C 2) -f (x ) d t R V

(2)

1 变型蔡氏电路的工作原理与实现方法

蔡氏双涡旋混沌吸引子的数学模型可以用式(1) 表示:

=a(y -x -f (x ) c ) d S =x -y +z (1) d S =-b y d S

式中, f (x ) c =vx +(u -v ) (|x +1|-|x -1|) /2, a 、b 、u 和v 为参数。

设Z =R V i L , U C 1=y , U C 2=x , t =C 1R V S , R V f (x ) =f (x ) c , R V g(U C 1) =g (U C 1) c , 则

=a(y -x -f (x ) c ) d S =x -y +z +g (y ) c (3) d S =-by d S

C 1

式中, a ==10, b =C 1R 2L /L =18, f (x ) c =C 2

vx +(u -v ) (|x +1|-|x -1|) /2,

收稿日期:2005-07-12 改回日期:2005-11-10

作者简介:孙福艳(1979-) , 女, 黑龙江省海伦市人, 硕士研究生, 研究方向:混沌控制理论及其在保密通信中的应用。

第2期孙福艳等:变型蔡氏混沌电路的实现

u =-1137, v =-0174,

非线形元器件

my y [0

g (y ) c = m 、n 为参数。

ny y >0

(3) 式来表示, 其中, 非线性器件N1为蔡氏二极管, 其原理如图2所示, N2也是一个非线形元件, 它能够实现非线形函数g (y ) c 的特性, 非线性元件

N2由两个受二极管控制的分段线性电阻和一个线性负阻并联构成, 其原理如图3

所示, 适当调整电阻R1和R2的阻值, 就可以得到不同的参数值。

实验结果

使用PSPICE911对所实现的变型蔡氏电路进行仿真模拟研究, 在C2两端输出的结果如图5所示:

图5 变型蔡氏电路仿真输出图形

严格来说, 使用PSPICE911进行的仿真仍然是一种数据仿真, 它使用的仿真模型直接来自于实际硬件电路模型, 仿真结果是与示波器从实际硬件电路得到的结果是相近的。但是实际蔡氏电路会受外界许多因素的影响, 比如电源不稳定、人为调整电阻R1、R2和

R20阻值的偏差等, 故C2两端输出的波形与实际的波形很难完全一样。通过实际硬件电路可以得到

C2两端单次触发输出的波形如图6、图7所示:

图2 蔡氏二极管N1的电路原理图

图3 非线形元件N2的电路原理图

变型蔡氏电路总体的电路图如图4所示:

图6 C2两端输出信号(时域图)

图4 变型蔡氏电路的电路原理图

图7 C 2两端输出信号

西华大学学报#自然科学版2006年

3 结论

本文作者提出了一种混沌发生器模型并对其进行了理论分析、仿真和硬件电路实现研究, 结果证明这种变型蔡氏电路为混沌通信和混沌现象的研究提供了一种新的混沌发生器。

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(责任编辑:夏书林)

(上接38页)

3) 综合评判。对于信息无关量集合I 上的模糊集A ={a 1, a 2, , , a n }, 通过R 变换为趋向集上的模糊集, 即

B =A #R ={b 1, b 2, , , b m }

机器人足球队伍的智能化水平(主要表现为有效的团队协作以及高智能化的对抗水平) 。

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[4]薛方正, 曹洋, 高大志. 东北大学机器人足球队决策系统设计[J]. 机器人, 2004, (11).

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式中b j . =b j /i 6 (j =1, 2, ... , m ) 。根据总体动=1作B c 趋向及最大隶属原则, 就可以对球员做出角色分配。

4) 计算综合决策值。即

N =B c#C

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[9]柳长安, 刘春阳, 李国栋. 基于模糊综合决策的足球机器人策略子系统[J]. 哈尔滨工业大学学报, 2004, (7) .

式中C ={c 1, c 2,.. . , c m }是动作趋向集的一个权重分配, C T 是C 的转置矩阵。按普通矩阵的乘法, 就

可以得到综合决策值, 最后根据其值的大小便可找适合该对手的最佳策略。

3 结论

仿真实验的结果表明, 该策略针对不同的对手, 可以有效的抑制对手水平的正常发挥, 增强了己方

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No. 2Journal of Xihua University #Natural Science 3

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