申明：以下各程序为个人在网络上收集的Lyapunov指数计算程序，未经过验证，不保证程序的正确性和计算结果的正确性，请大家见谅，也欢迎大家探讨！
一、计算连续方程Lyapunov指数的程序
二、wolf 方法计算李雅普诺夫指数
三、小数据量法计算Lyapunov指数的 Matlab 程序
四、C-C方法计算时间延迟和嵌入维数计算Lyapunov指数计算关联维数混沌时
五、计算各种混沌系统李雅普洛夫指数的MATLAB源程序
六、二维Henon映射的Lyapunov指数的计算
一、计算连续方程Lyapunov指数的程序，比较好用的
其中给出了两个例子： 计算Rossler吸引子的Lyapunov指数 计算超混沌Rossler吸引子的Lyapunov指数 www.pudn/downloads39/sourcecode/math/detail132231.html 基于Volterra滤波器混沌时间序列多步预测 ---------------------------------------------- 参考文献： 1、张家树.混沌时间序列的Volterra自适应预测.物理学报.2000.03 2、Scott C.Douglas, Teresa H.-Y. Meng, Normalized Data Nonlinearities for LMS Adaptation. IEEE Trans.Sign.Proc. Vol.42 1994 ---------------------------------------------- 文件说明： 1、original_MultiStepPred_main.m 程序主文件,直接运行此文件即可 2、original_train.m 训练函数 3、original_test.m 测试函数 4、LorenzData.dll 产生Lorenz离散序列 5、normalize_1.m 归一化 6、PhaSpaRecon.m 相空间重构 7、PhaSpa2VoltCoef.m 构造 Volterra 自适应 FIR 滤波器的输入信号矢量 Un 8、TrainTestSample_2.m 将特征矩阵前 train_num 个为训练样本，其余为测试样本 9、FIR_NLMS.dll NLMS自适应算法 www.pudn/downloads45/sourcecode/math/detail150408.html |
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recnstitution重构相空间，在非线性系统分析中有重要的作用
MATLAB程序如下：
1function [Texp,Lexp]=lyapunov(n,tstart,stept,tend,ystart,ioutp);
2global DS;
3global P;
4global calculation_progress first_call;
5global driver_window;
6global TRJ_bufer Time_bufer bufer_i;
7
8%
9% Lyapunov exponent calcullation for ODE-system.
10%
11% The alogrithm employed in this m-file for determining Lyapunov
12% exponents was proposed in
13%
14% A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano,
15% "Determining Lyapunov Exponents from a Time Series," Physica D,
16% Vol. 16, pp. 285-317, 1985.
17%
18% For integrating ODE system can be used any MATLAB ODE-suite methods.
19% This function is a part of MATDS program - toolbox for dynamical system investigation
20% See: www.math.rsu.ru/mexmat/kvm/matds/
21%
22% Input parameters:
23% n - number of equation
24% rhs_ext_fcn - handle of function with right hand side of extended ODE-system.
25% This function must include RHS of ODE-system coupled with
26% variational equation (n items of linearized systems, see Example).
27% fcn_integrator - handle of ODE integrator function, for example: @ode45
28% tstart - start values of independent value (time t)
29% stept - step on t-variable for Gram-Schmidt renormalization procedure.
30% tend - finish value of time
31% ystart - start point of trajectory of ODE system.
32% ioutp - step of print to MATLAB main window. ioutp==0 - no print,
33% if ioutp>0 then each ioutp-th point will be print.
34%
35% Output parameters:
36% Texp - time values
37% Lexp - Lyapunov exponents to each time value.
38%
39% Users have to write their own ODE functions for their specified
40% systems and use handle of this function as rhs_ext_fcn - parameter.
41%
42% Example. Lorenz system:
43% dx/dt = sigma*(y - x) = f1
44% dy/dt = r*x - y - x*z = f2
45% dz/dt = x*y - b*z = f3
46%
47% The Jacobian of system:
48% | -sigma sigma 0 |
49% J = | r-z -1 -x |
50% | y x -b |
51%
52% Then, the variational equation has a form:
53%
54% F = J*Y
55% where Y is a square matrix with the same dimension as J.
maxstep56% Corresponding m-file:
57% function f=lorenz_ext(t,X)
58% SIGMA = 10; R = 28; BETA = 8/3;
59% x=X(1); y=X(2); z=X(3);
60%
61% Y= [X(4), X(7), X(10);
62% X(5), X(8), X(11);
63% X(6), X(9), X(12)];
64% f=zeros(9,1);
65% f(1)=SIGMA*(y-x); f(2)=-x*z+R*x-y; f(3)=x*y-BETA*z;
66%
67% Jac=[-SIGMA,SIGMA,0; R-z,-1,-x; y, x,-BETA];
68%
69% f(4:12)=Jac*Y;
70%
71% Run Lyapunov exponent calculation:
72%
73% [T,Res]=lyapunov(3,@lorenz_ext,@ode45,0,0.5,200,[0 1 0],10);
74%
75% See files: lorenz_ext, run_lyap.
76%
77% --------------------------------------------------------------------
78% Copyright (C) 2004, Govorukhin V.N.
79% This file is intended for use with MATLAB and was produced for MATDS-program
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