基于线性反馈控制的混沌非同元系统的同步研究

function fractional_chaos clear all; close all; clc; Dim=6;q=[sqrt(3)/2;0.8;1.1;sqrt(3)/2;0.8;1.1]; h=0.01;FinalTime=100;t=0:h:FinalTime;N=length(t)-1;u=0:h:FinalTime+h; x_0=[0.1 0.2 0.3 0.4 0.5 0.6]; x0=[x_0]'; x(:,1)=x0; a=zeros(Dim,N);b=zeros(Dim,N+1); T1=(h.^q./q)./gamma(q); T2=(h.^q)./gamma(q+2); for n=1:N for m=1:Dim a(m,N+1-n)=(n+1)^(q(m)+1)+(n-1)^(q(m)+1)-2*n^(q(m)+1); b(m,N+1-n)=(n+1)^q(m)-n^q(m); a0(m,n+1)=n^(q(m)+1)-(n-q(m))*(n+1)^q(m); end end b(:,N+1)=1;a0(:,1)=q; %a=repmat(aj,Dim,1); %b=repmat(bj,Dim,1); for n=0:N OUT1(:,n+1)=fx(x(:,n+1)); if(n==0) sum2=a0(:,n+1).*fx(x0); else sum2=sum(a(:,N+1-n:end).*OUT1(:,2:n+1),2)+a0(:,n+1).*fx(x0); end sum1=sum(b(:,N+1-n:end).*OUT1(:,1:n+1),2); xp=x0+T1.*sum1; x(:,n+2)=x0+T2.*fx(xp)+T2.*sum2; if(mod(n,100)==0) disp([x(:,n+2)' n/N]); end end % plot(x(1,500:end),x(2,500:end)) % xlabel('x_1'),ylabel('x_2') % figure,plot(x(1,500:end),x(3,500:end)) % xlabel('x_1'),ylabel('x_3') % figure,plot(x(2,500:end),x(3,500:end)) % xlabel('x_2'),ylabel('x_3') % figure,plot3(x(1,500:end),x(2,500:end),x(3,500:end)) % xlabel('x_1'),ylabel('x_2'),zlabel('x_3') % figure,plot(x(2,100:end),x(3,100:end)) % xlabel('x_1'),ylabel('x_2') % % figure,plot(u,x(1,1:end)) % xlabel('u'),ylabel('x1') % figure,plot(u,x(2,1:end)) % xlabel('u'),ylabel('x2') % figure,plot(u,x(3,1:end)) % xlabel('u'),ylabel('x3') save e_h_5.mat x function OUT=fx(X) x1=X(1); x2=X(2); x3=X(3); x4=X(4); x5=X(5); x6=X(6); DX1=[x2; x3; -6*x1-2.92*x2-1.2*x3+x1^2; x5-90*(x4-x1); x6-30*(x5-x2); -6*x4-2.92*x5-1.2*x6+x4^2-7.88*(x6-x3);]; OUT=[DX1(:)];