求最大lyapunov指数时用LET工具箱求出和用时序数列算出结果不一致怎么解释？
我用LET工具箱算最大lyapunov指数为1.5，然后用一组时序数列反过来算最大lyapunov指数的结果只有0.6。为什么会有这么大的误差，是系统的信息丢失问题还是程序的问题抑或其他？还有一个小疑问，相空间重构之后的嵌入维数是不是对应最大lyapunov的个数，那m与方程的元数又有什么关系呢？
function =largest_lyapunov_exponent(data,N,m,tau,P,delt_t)
%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
%delt_t:Sampling interval
%lambda_1:return the largest lyapunov exponent
%skyhawk
%delt_t=0.01;
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
=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,'-o',x,yp,'--')
页:
[1]