利亚诺夫指数代码.zip_李亚帊诺夫_李亚诺夫指数_李亚诺夫指数；matlab

function lambda_1=largest_lyapunov_exponent(data) %the function is used to calcultate largest lyapunov exponent with the %mended algorithm,which put forward by lv jing hu. %data:the time series %N:the length of data %m:enbedding dimention %tau:time delay %P:the mean period of the time series,calculated with FFT %lambda_1:return the largest lyapunov exponent %skyhawk N=length(data); m=7; tau=14; P=50; delt_t=1; idx_j=0; Y=reconstitution(data,N,m,tau );%reconstitute state space M=N-(m-1)*tau;%M is the number of embedded points in m-dimensional space for j=1:M d_max=1e+100; for jj=1:M %寻找相空间中每个点的最近距离点，并记下 d_s=0; %该点下标 if abs(j-jj)>P %限制短暂分离 for i=1:m d_s=d_s+(Y(i,j)-Y(i,jj))*(Y(i,j)-Y(i,jj)); d_min=d_max; if d_s<d_min d_min=d_s; idx_j=jj; end end end end %index(j)=idx_j; max_i=min((M-j),(M-idx_j));%计算点j的最大演化时间步长i for k=1:max_i %计算点j与其最近邻点在i个离散步后的距离 d_j_i=0; for kk=1:m d_j_i=d_j_i+(Y(kk,j+k)-Y(kk,idx_j+k))*(Y(kk,j+k)-Y(kk,idx_j+k)); d(k,j)=d_j_i; end end end %对每个演化时间步长i，求所有的j的lnd(i,j)平均 [l_i,l_j]=size(d); for i=1:l_i q=0; y_s=0; for j=1:l_j if d(i,j)~=0 q=q+1; y_s=y_s+log(d(i,j)); end end y(i)=y_s/(q*delt_t); end x=1:length(y); pp=polyfit(x,y,1); lambda_1=pp(1); yp=polyval(pp,x); plot(x,y,'r',x,yp,'--')