c_cmethod.m

这个是在进行混沌时间序列分析时的C-C算法的matlab程序

p=16;
r=45.92;
b=4.0;
x(1)=10;
y(1)=1;
z(1)=0;
h=0.01;
for i=1:10000
    K1=p*(y(i)-x(i));
    L1=r*x(i)-y(i)-x(i)*z(i);
    M1=-b*z(i)+x(i)*y(i);
    
    K2=p*((y(i)+h/2*L1)-(x(i)+h/2*K1));
    L2=r*(x(i)+h/2*K1)-(y(i)+h/2*L1)-(x(i)+h/2*K1)*(z(i)+h/2*M1);
    M2=-b*(z(i)+h/2*M1)+(x(i)+h/2*K1)*(y(i)+h/2*L1);
    
    K3=p*((y(i)+h/2*L2)-(x(i)+h/2*K1));
    L3=r*(x(i)+h/2*K1)-(y(i)+h/2*L2)-(x(i)+h/2*K1)*(z(i)+h/2*M2);
    M3=-b*(z(i)+h/2*M1)+(x(i)+h/2*K1)*(y(i)+h/2*L2);
    
    K4=p*((y(i)+h*L3)-(x(i)+h*K3));
    L4=r*(x(i)+h*K3)-(y(i)+h*L3)-(x(i)+h*K3)*(z(i)+h*M3);
    M4=-b*(z(i)+h*M3)+(x(i)+h*K3)*(y(i)+h*L3);
    
    x(i+1)=x(i)+h/6*(K1+2*K2+2*K3+K4);
    y(i+1)=y(i)+h/6*(L1+2*L2+2*L3+L4);
    z(i+1)=z(i)+h/6*(M1+2*M2+2*M3+M4);
end
for i=1:3000
    data(i)=x(i+5000);
end
figure(1)
plot(data);
%function [s,delt_s,s_cor]=C_CMethod(data)
%this function calculate time delay and embedding demension with C-C
%Method,which proved by H.S.Kim
%skyhawk&flyinghawk
% %****************调试程序段****************************
% clear all;
% data=load('f:/sunpot/year sunpot number.txt');
% %************************************************

N=length(data);
max_d=200;%the maximum value of the time delay

sigma=std(data);%calcute standard deviation s_d

for t=1:max_d
    t
    s_t=0;
    delt_s_s=0;
    for m=2:5
        s_t1=0;
        for j=1:4
            r=sigma*j/2;
            data_d=disjoint(data,N,t);%将时间序列分解成t个不相交的时间序列
            [ll,N_d]=size(data_d);
            s_t3=0;
            for i=1:t
                %i
                Y=data_d(i,:);
                C_1(i)=correlation_integral(Y,N_d,r);%计算C(1,N_d,r,t)
                %X=reconstitution(Y,N_d,m,t);%相空间重构
                M=N_d-(m-1);  %相空间中点的个数
                for ii=1:m      %相空间的维数
                    for jj=1:M           %相空间重构的点数目 
                        X(ii,jj)=Y((ii-1)+jj);
                    end
                end
                N_r=N_d-(m-1);
                C_I(i)=correlation_int(X,N_r,m,r);%计算C(m,N_r,r,t)
                s_t3=s_t3+(C_I(i)-C_1(i)^m);%对t个不相关的时间序列求和
            end
            s_t2(j)=s_t3/t;
            s_t1=s_t1+s_t2(j);%对rj求和
        end
        delt_s_m(m)=max(s_t2)-min(s_t2);%求delt S(m,t)
        delt_s_s=delt_s_s+delt_s_m(m);%delt S(m,t)对m求和
        s_t0(m)=s_t1;
        s_t=s_t+s_t0(m);%S对m求和
    end
    s(t)=s_t/16;
    delt_s(t)=delt_s_s/4;       %delt S的平均值
    s_cor(t)=delt_s(t)+abs(s(t));  %delt S
   
end
figure(2)
plot(s);
xlabel('t'),ylabel('S(t)')
title('Lorenz序列C-C算法');
grid;
figure(3)
plot(delt_s);
xlabel('t'),ylabel('delt-S(t)')
title('Lorenz序列C-C算法');
grid;
figure(4)
plot(s_cor);
xlabel('t'),ylabel('delt-S-cor(t)')
title('Lorenz序列C-C算法');
grid;
s1=s';
data1=data';
delt_s1=delt_s';
s_cor1=s_cor';