main_boxdimension_ts.m

计算混沌系统的lyapunov指数和poincare截面

% 计算时间序列的盒维数 - 主函数

clc
clear all
close all

%--------------------------------------------------------------------------
% produce the FBM time series，Set parameter H to 0.6 and sample length

rand('state',sum(100*clock))
H = 0.6; lg = 1024;
s = wfbm(H,lg);                    % 时间序列

figure; plot(s,'.-')

%--------------------------------------------------------------------------

partition = 2^7;                   % 每一维坐标上的分割数
[log2_C,log2_r] = BoxDimension_TS(s,partition);

%--------------------------------------------------------------------------

figure
plot(log2_r,log2_C,'bo'); xlabel('log_2(r)'); ylabel('log_2(C(r))'); hold on;

% 确定线性区域
Linear = 1:length(log2_C);
par = polyfit(log2_r(Linear),log2_C(Linear),1);
Df = par(1)              % 盒维数

log2_C_estimate = polyval(par,log2_r(Linear),1);
plot(log2_r(Linear),log2_C_estimate,'r-'); hold off;