www.pudn.com > Chaos_Prediction.rar > Main_CorrelationDimension_GP.m

% G-P 算法求关联维(输入时间序列数据)
% 使用平台 - Matlab6.5 / Matlab7.0
% 作者：陆振波，海军工程大学
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clc
clear all
close all

%--------------------------------------------------------------------------
% 产生 Lorenz 时间序列
% dx/dt = sigma*(y-x)
% dy/dt = r*x - y - x*z
% dz/dt = -b*z + x*y

sigma = 16;             % Lorenz方程参数
r = 45.92;               
b = 4;          

y = [-1;0;1];           % 起始点 (3x1 的列向量)
h = 0.01;               % 积分时间步长

k1 = 30000;             % 前面的迭代点数
k2 = 5000;              % 后面的迭代点数

X = LorenzData(y,h,k1+k2,sigma,r,b);
X = X(k1+1:end,1);      % 时间序列(列向量)

%--------------------------------------------------------------------------
% G-P算法计算关联维

rr = 0.5;
Log2R = -6:rr:0;        % log2(r)
R = 2.^(Log2R);

t = 10;                 % 时延
dd = 1;                 % 嵌入维间隔
D = 2:dd:10;            % 嵌入维    
p = 50;                 % 限制短暂分离，大于序列平均周期(不考虑该因素时 p = 1)   

tic 
Log2Cr = log2(CorrelationIntegral(X,t,D,R,p));       % 输出每一行对应一个嵌入维
toc

%--------------------------------------------------------------------------
% 结果作图

figure
plot(Log2R,Log2Cr','k.-'); axis tight; grid on; hold on;
xlabel('log2(r)'); 
ylabel('log2(C(r))');
title(['Lorenz, length = ',num2str(k2)]);

%--------------------------------------------------------------------------
% 最小二乘拟合

Linear = [3:9];                       % 线性似合区域
[A,B] = LM1(Log2R,Log2Cr,Linear);     % 最小二乘求斜率

for i = 1:length(D)
    Y = polyval([A(i),B(i)],Log2R(Linear),1);
    plot(Log2R(Linear),Y,'r');    
end
hold off;

%--------------------------------------------------------------------------
% 求梯度

Slope = diff(Log2Cr,1,2)/rr;           % 求梯度
xSlope = Log2R(1:end-1);               % 梯度所对应的log2(r)

figure;
plot(xSlope,Slope','k.-'); axis tight; grid on;
xlabel('log2(r)'); 
ylabel('slope');
title(['Lorenz, length = ',num2str(k2)]);

%--------------------------------------------------------------------------
% 关联维曲线

figure;
plot(D,A,'k.-'); grid on; axis tight;
xlabel('m'); 
ylabel('Correlation Dimension');
title(['Lorenz, length = ',num2str(k2)]);