求最大李雅普诺夫指数的matlab程序

求最大李雅普诺夫指数的matlab程序 程序一 function dx=Lorenz(t,x); dx(1,1)=10*(x(2)-x(1)); dx(2,1)=x(1)*(30-x(3))-x(2); dx(3,1)=x(1)*x(2)-8/3*x(3); dx(4,1)=0; dx(5,1)=0; dx(6,1)=0; function lambda_1=lyapunov_wolf1(data,N,m,tau,P) % 该函数用来计算时间序列的最大Lyapunov 指数--Wolf 方法 % m: 嵌入维数 % tau:时间延迟 % data:时间序列 % N:时间序列长度 % P:时间序列的平均周期,选择演化相点距当前点的位置差，即若当前相点为I，则演化相点只能在|I,J|>P的相点中搜寻 % lambda_1:返回最大lyapunov指数值 %************************************************************************** % ode计算整数阶系统的时间序列 %****************************************************************** delt_t1 = 0.001; t1 = 0:delt_t1:60; [tt1,y1]=ode45(@lorenz,t1,[-1,0,1]); xx1 = y1(:,1)'; x1 = spline(tt1, xx1, t1); data= x1(20000:10:60000);%采样 N=length(data); m=3; tau=11; %***************************************************** % FFT计算平均周期 %********************************************************** x=data; xPower=abs(fft(x)).^2; NN=length(xPower); xPower(1)=[];%去除直流分量 NN=floor(NN/2); xPower=xPower(1:NN); freq=(1:NN)/NN*0.5; [mP,index]=max(xPower); P=index; %************************************************************* strengthen the sense of responsibility, work to solve the lack of decent occupation explain away, conduct problems. To establish the overall concept, eliminate departmentalism. Strict assessment and accountability, to solve the spiritual slack, nianqingpazhong, status quo, and other issues. To establish and perfect the muddle along Bureau staff conduct work regulations, standardize the behavior of personnel. 2. To strengthen the responsibility system. One is the in-depth study and implement the "Hunan provincial Party and government leading cadres Interim Provisions on the work safety of a pair of > (Hunan Office issued 2013 No. 5)," Hunan province safety supervision and management responsibilities of the provisions on the production (Hunan Zhengban made 2013 No. 4) And resolutely implement the safety production of the party with responsibility, a pair of responsibility. "Two is issued safety production administration and inspection to promote the responsibilities bear safety production supervision departments strictly and effectively assumed responsibility. The three is to establish risk self correction self reporting system for safety in production enterprises, promote the enterprises to implement the main responsibility for production safety is introduced. Four strengthen the county safety production supervision ability construction work, promote safe production responsibility to the grassroots. 3, strict accountability and target management. Adhere to the" who is in charge, who is responsible for the pipe industry must be safe, Guan Sheng production and operation must be safe, pipe business must control security "principle, the implementation of safety The production of "cure." stagnation supervision and leadership responsible system. The safety production of key towns, key enterprises and key problems, by the township government and the Department responsible for the stagnation led the lump sum, to tackle tough. To further increase the production safety index assessment, strictly implement the safety production of the "one vote veto" and the reward system, strengthen the safety incentive and restraint mechanism. (six) the implementation of the work force is not strong. The documents, meeting, long work arrangement, check and supervise the implementation of small, poor implementation of the system, the work is not effective. Some leading cadres sense of purpose, consciousness of the masses is not strong, the ruling " For the people "," the interests of the masses no matter "concept understanding is not in place. The specific work treats with the deployment, a few leading cadres complain that work is too complicated, too much responsibility, the pressure is too large, too much emphasis on the difficulty of the work, such as underground mines to avoid the disaster of" six systems "construction and construction of mechanical ventilation to file the form, forwarding arrangements work, no in-depth mining enterprises to promote the specific work, the increase in the number of files, but the effect is not good, not according to the actual situation of non coal mines in the county, to engage in" across the board ", and the quality min_point=1 ; %&&要求最少搜索到的点数 MAX_CISHU=5 ; %&&最大增加搜索范围次数 %FLYINGHAWK % 求最大、最小和平均相点距离 max_d = 0; %最大相点距离 min_d = 1.0e+100; %最小相点距离 avg_dd = 0; Y=reconstitution(data,N,m,tau); %相空间重构 M=N-(m-1)*tau; %重构相空间中相点的个数 for i = 1 : (M-1) for j = i+1 : M d = 0; for k = 1 : m d = d + (Y(k,i)-Y(k,j))*(Y(k,i)-Y(k,j)); end d = sqrt(d); if max_d < d max_d = d; end if min_d > d min_d = d; end avg_dd = avg_dd + d; end end avg_d = 2*avg_dd/(M*(M-1)); %平均相点距离 dlt_eps = (avg_d - min_d) * 0.02 ; %若在min_eps,max_eps中找不到演化相点时，对max_eps的放宽幅度 min_eps = min_d + dlt_eps / 2 ; %演化相点与当前相点距离的最小限 max_eps = min_d + 2 * dlt_eps ; %&&演化相点与当前相点距离的最大限 % 从P+1,M-1个相点中找与第一个相点最近的相点位置(Loc_DK)及其最短距离DK DK = 1.0e+100; %第i个相点到其最近距离点的距离 Loc_DK = 2; %第i个相点对应的最近距离点的下标 for i = (P+1):(M-1) %限制短暂分离，从点P+1开始搜索 d = 0; for k = 1 : m d = d + (Y(k,i)-Y(k,1))*(Y(k,i)-Y(k,1)); end d = sqrt(d); if (d < DK) & (d > min_eps) DK = d; Loc_DK = i; strengthen the sense of responsibility, work to solve the lack of decent occupation explain away, conduct problems. To establish the overall concept, eliminate departmentalism. Strict assessment and accountability, to solve the spiritual slack, nianqingpazhong, status quo, and other issues. To establish and perfect the muddle along Bureau staff conduct work regulations, standardize the behavior of personnel. 2. To strengthen the responsibility system. One is the in-depth study and implement the "Hunan provincial Party and government leading cadres Interim Provisions on the work safety of a pair of > (Hunan Office issued 2013 No. 5)," Hunan province safety supervision and management responsibilities of the provisions on the production (Hunan Zhengban made 2013 No. 4) And resolutely implement the safety production of the party with responsibility, a pair of responsibility. "Two is issued safety production administration and inspection to promote the responsibilities bear safety production supervision departments strictly and effectively assumed responsibility. The three is to establish risk self correction self reporting system for safety in production enterprises, promote the enterprises to implement the main responsibility for production safety is introduced. Four strengthen the county safety production supervision ability construction work, promote safe production responsibility to the grassroots. 3, strict accountability and target management. Adhere to the" who is in charge, who is responsible for the pipe industry must be safe, Guan Sheng production and operation must be safe, pipe business must control security "principle, the implementation of safety The production of "cure." stagnation supervision and leadership responsible system. The safety production of key towns, key enterprises and key problems, by the township government and the Department responsible for the stagnation led the lump sum, to tackle tough. To further increase the production safety index assessment, strictly implement the safety production of the "one vote veto" and the reward system, strengthen the safety incentive and restraint mechanism. (six) the implementation of the work force is not strong. The documents, meeting, long work arrangement, check and supervise the implementation of small, poor implementation of the system, the work is not effective. Some leading cadres sense of purpose, consciousness of the masses is not strong, the ruling " For the people "," the interests of the masses no matter "concept understanding is not in place. The specific work treats with the deployment, a few leading cadres complain that work is too complicated, too much responsibility, the pressure is too large, too much emphasis on the difficulty of the work, such as underground mines to avoid the disaster of" six systems "construction and construction of mechanical ventilation to file the form, forwarding arrangements work, no in-depth mining enterprises to promote the specific work, the increase in the number of files, but the effect is not good, not according to the actual situation of non coal mines in the county, to engage in" across the board ", and the quality end end % 以下计算各相点对应的李氏数保存到lmd()数组中 % i 为相点序号，从1到(M-1)，也是i-1点的演化点;Loc_DK为相点i-1对应最短距离的相点位置，DK为其对应的最短距离 % Loc_DK+1为Loc_DK的演化点，DK1为i点到Loc_DK+1点的距离，称为演化距离 % 前i个log2(DK1/DK)的累计和用于求i点的lambda值 sum_lmd = 0 ; % 存放前i个log2(DK1/DK)的累计和 for i = 2 : (M-1) % 计算演化距离 DK1 = 0; for k = 1 : m DK1 = DK1 + (Y(k,i)-Y(k,Loc_DK+1))*(Y(k,i)-Y(k,Loc_DK+1)); end DK1 = sqrt(DK1); old_Loc_DK = Loc_DK ; % 保存原最近位置相点 old_DK=DK; % 计算前i个log2(DK1/DK)的累计和以及保存i点的李氏指数 if (DK1 ~= 0)&( DK ~= 0) sum_lmd = sum_lmd + log(DK1/DK) /log(2); end lmd(i-1) = sum_lmd/(i-1); % 以下寻找i点的最短距离:要求距离在指定距离范围内尽量短，与DK1的角度最小 point_num = 0 ; % &&在指定距离范围内找到的候选相点的个数 cos_sita = 0 ; %&&夹角余弦的比较初值 ——要求一定是锐角 zjfwcs=0 ;%&&增加范围次数 while (point_num == 0) % * 搜索相点 for j = 1 : (M-1) if abs(j-i) <=(P-1) %&&候选点距当前点太近，跳过～ continue; end %*计算候选点与当前点的距离 dnew = 0; for k = 1 : m dnew = dnew + (Y(k,i)-Y(k,j))*(Y(k,i)-Y(k,j)); end dnew = sqrt(dnew); if (dnew < min_eps)|( dnew > max_eps ) %&&不在距离范围，跳过～ continue; end %*计算夹角余弦及比较 strengthen the sense of responsibility, work to solve the lack of decent occupation explain away, conduct problems. To establish the overall concept, eliminate departmentalism. Strict assessment and accountability, to solve the spiritual slack, nianqingpazhong, status quo, and other issues. To establish and perfect the muddle along Bureau staff conduct work regulations, standardize the behavior of personnel. 2. To strengthen the responsibility system. One is the in-depth study and implement the "Hunan provincial Party and government leading cadres Interim Provisions on the work safety of a pair of > (Hunan Office issued 2013 No. 5)," Hunan province safety supervision and management responsibilities of the provisions on the production (Hunan Zhengban made 2013 No. 4) And resolutely implement the safety production of the party with responsibility, a pair of responsibility. "Two is issued safety production administration and inspection to promote the responsibilities bear safety production supervision departments strictly and effectively assumed responsibility. The three is to establish risk self correction self reporting system for safety in production enterprises, promote the enterprises to implement the main responsibility for production safety is introduced. Four strengthen the county safety production supervision ability construction work, promote safe production responsibility to the grassroots. 3, strict accountability and target management. Adhere to the" who is in charge, who is responsible for the pipe industry must be safe, Guan Sheng production and operation must be safe, pipe business must control security "principle, the implementation of safety The production of "cure." stagnation supervision and leadership responsible system. The safety production of key towns, key enterprises and key problems, by the township government and the Department responsible for the stagnation led the lump sum, to tackle tough. To further increase the production safety index assessment, strictly implement the safety production of the "one vote veto" and the reward system, strengthen the safety incentive and restraint mechanism. (six) the implementation of the work force is not strong. The documents, meeting, long work arrangement, check and supervise the implementation of small, poor implementation of the system, the work is not effective. Some leading cadres sense of purpose, consciousness of the masses is not strong, the ruling " For the people "," the interests of the masses no matter "concept understanding is not in place. The specific work treats with the deployment, a few leading cadres complain that work is too complicated, too much responsibility, the pressure is too large, too much emphasis on the difficulty of the work, such as underground mines to avoid the disaster of" six systems "construction and construction of mechanical ventilation to file the form, forwarding arrangements work, no in-depth mining enterprises to promote the specific work, the increase in the number of files, but the effect is not good, not according to the actual situation of non coal mines in the county, to engage in" across the board ", and the quality DOT = 0; for k = 1 : m DOT = DOT+(Y(k,i)-Y(k,j))*(Y(k,i)-Y(k,old_Loc_DK+1)); end CTH = DOT/(dnew*DK1); if acos(CTH) > (3.14151926/4) %&&不是小于45度的角，跳过～ continue; end if CTH > cos_sita %&&新夹角小于过去已找到的相点的夹角，保留 cos_sita = CTH; Loc_DK = j; DK = dnew; end point_num = point_num +1; end if point_num <= min_point max_eps = max_eps + dlt_eps; zjfwcs =zjfwcs +1; if zjfwcs > MAX_CISHU %&&超过最大放宽次数，改找最近的点 DK = 1.0e+100; for ii = 1 : (M-1) if abs(i-ii) <= (P-1) %&&候选点距当前点太近，跳过～ continue; end d = 0; for k = 1 : m d = d + (Y(k,i)-Y(k,ii))*(Y(k,i)-Y(k,ii)); end d = sqrt(d); if (d < DK) & (d > min_eps) DK = d; Loc_DK = ii; end end break; end point_num = 0 ; %&&扩大距离范围后重新搜索 cos_sita = 0; end strengthen the sense of responsibility, work to solve the lack of decent occupation explain away, conduct problems. To establish the overall concept, eliminate departmentalism. Strict assessment and accountability, to solve the spiritual slack, nianqingpazhong, status quo, and other issues. To establish and perfect the muddle along Bureau staff conduct work regulations, standardize the behavior of personnel. 2. To strengthen the responsibility system. One is the in-depth study and implement the "Hunan provincial Party and government leading cadres Interim Provisions on the work safety of a pair of > (Hunan Office issued 2013 No. 5)," Hunan province safety supervision and management responsibilities of the provisions on the production (Hunan Zhengban made 2013 No. 4) And resolutely implement the safety production of the party with responsibility, a pair of responsibility. "Two is issued safety production administration and inspection to promote the responsibilities bear safety production supervision departments strictly and effectively assumed responsibility. The three is to establish risk self correction self reporting system for safety in production enterprises, promote the enterprises to implement the main responsibility for production safety is introduced. Four strengthen the county safety production supervision ability construction work, promote safe production responsibility to the grassroots. 3, strict accountability and target management. Adhere to the" who is in charge, who is responsible for the pipe industry must be safe, Guan Sheng production and operation must be safe, pipe business must control security "principle, the implementation of safety The production of "cure." stagnation supervision and leadership responsible system. The safety production of key towns, key enterprises and key problems, by the township government and the Department responsible for the stagnation led the lump sum, to tackle tough. To further increase the production safety index assessment, strictly implement the safety production of the "one vote veto" and the reward system, strengthen the safety incentive and restraint mechanism. (six) the implementation of the work force is not strong. The documents, meeting, long work arrangement, check and supervise the implementation of small, poor implementation of the system, the work is not effective. Some leading cadres sense of purpose, consciousness of the masses is not strong, the ruling " For the people "," the interests of the masses no matter "concept understanding is not in place. The specific work treats with the deployment, a few leading cadres complain that work is too complicated, too much responsibility, the pressure is too large, too much emphasis on the difficulty of the work, such as underground mines to avoid the disaster of" six systems "construction and construction of mechanical ventilation to file the form, forwarding arrangements work, no in-depth mining enterprises to promote the specific work, the increase in the number of files, but the effect is not good, not according to the actual situation of non coal mines in the county, to engage in" across the board ", and the quality end end %取平均得到最大李雅普诺夫指数 lambda_1=sum(lmd)/length(lmd) function X=reconstitution(data,N,m,tau) %该函数用来重构相空间 % m为嵌入空间维数 % tau为时间延迟 % data为输入时间序列 % N为时间序列长度 % X为输出,是m*n维矩阵 M=N-(m-1)*tau;%相空间中点的个数 for j=1:M %相空间重构 for i=1:m X(i,j)=data((i-1)*tau+j); end end 以上是计算最大李氏指数的程序，可以运行。问题是里面的时间延迟tau和嵌入维数m该如何取值，程序里我是随便取的3和11 ******************************************************************************* 程序二 现我做了一个基于RHR算法的李氏指数计算方法，收敛速度很快，精确度也还可以，现传上: Lya1=[];Lya2=[];Lya3=[]; V=eye(3); S=V;b1=0; a=0.4;c=0.2;gama=3.5; b=4.0; h=0.01; x(1)=0.1;y(1)=0;z(1)=0;n=0; while z<=200 n=n+1; k1=h*y(n); m1=h*(-sin(x(n))-a*y(n)+b*cos(gama*z(n)).*sin(x(n))+c); k2=h*(y(n)+m1/2); m2=h*(-sin(x(n)+k1/2)-a*(y(n)+m1/2)+b*cos(gama*(z(n)+h/2)).*sin(x(n)+k1/2)+c); k3=h*(y(n)+m2/2); m3=h*(-sin(x(n)+k2/2)-a*(y(n)+m2/2)+b*cos(gama*(z(n)+h/2)).*sin(x(n)+k2/2)+c); k4=h*(y(n)+m3); strengthen the sense of responsibility, work to solve the lack of decent occupation explain away, conduct problems. To establish the overall concept, eliminate departmentalism. Strict assessment and accountability, to solve the spiritual slack, nianqingpazhong, status quo, and other issues. To establish and perfect the muddle along Bureau staff conduct work regulations, standardize the behavior of personnel. 2. To strengthen the responsibility system. One is the in-depth study and implement the "Hunan provincial Party and government leading cadres Interim Provisions on the work safety of a pair of > (Hunan Office issued 2013 No. 5)," Hunan province safety supervision and management responsibilities of the provisions on the production (Hunan Zhengban made 2013 No. 4) And resolutely implement the safety production of the party with responsibility, a pair of responsibility. "Two is issued safety production administration and inspection to promote the responsibilities bear safety production supervision departments strictly and effectively assumed responsibility. The three is to establish risk self correction self reporting system for safety in production enterprises, promote the enterprises to implement the main responsibility for production safety is introduced. Four strengthen the county safety production supervision ability construction work, promote safe production responsibility to the grassroots. 3, strict accountability and target management. Adhere to the" who is in charge, who is responsible for the pipe industry must be safe, Guan Sheng production and operation must be safe, pipe business must control security "principle, the implementation of safety The production of "cure." stagnation supervision and leadership responsible system. The safety production of key towns, key enterprises and key problems, by the township government and the Department responsible for the stagnation led the lump sum, to tackle tough. To further increase the production safety index assessment, strictly implement the safety production of the "one vote veto" and the reward system, strengthen the safety incentive and restraint mechanism. (six) the implementation of the work force is not strong. The documents, meeting, long work arrangement, check and supervise the implementation of small, poor implementation of the system, the work is not effective. Some leading cadres sense of purpose, consciousness of the masses is not strong, the ruling " For the people "," the interests of the masses no matter "concept understanding is not in place. The specific work treats with the deployment, a few leading cadres complain that work is too complicated, too much responsibility, the pressure is too large, too much emphasis on the difficulty of the work, such as underground mines to avoid the disaster of" six systems "construction and construction of mechanical ventilation to file the form, forwarding arrangements work, no in-depth mining enterprises to promote the specific work, the increase in the number of files, but the effect is not good, not according to the actual situation of non coal mines in the county, to engage in" across the board ", and the quality m4=h*(-sin(x(n)+k3)-a*(y(n)+m3)+b*cos(gama*(z(n)+h)).*sin(x(n)+k3)+c); x(n+1)=x(n)+(k1+2*k2+2*k3+k4)/6; y(n+1)=y(n)+(m1+2*m2+2*m3+m4)/6; z(n+1)=n*h; J = [0 1 0; b*cos(gama*z(n+1))*cos(x(n+1))-cos(x(n+1)) -a -b*gama*sin(gama*z(n+1))*sin(x(n+1)); 0 0 0]; J=eye(3)+h*J; B=J*V*S; [V,S,U]=svd(B); a_max=max(diag(S)); S=(1/a_max)*S; b1=b1+log(a_max); Lyapunov1=(log(diag(S))+b1)/(n*h); Lya1=[Lya1,Lyapunov1(1,]; Lya2=[Lya2,Lyapunov1(2,]; Lya3=[Lya3,Lyapunov1(3,]; end Lyapunov1 n=1:20001; plot(n,Lya1,'k',n,Lya2,'k',n,Lya3,'k') %grid on axis([0,30001,-0.8,0.5]) title('Lyapunov exponents of Warship') xlabel('n'),ylabel('LCE') strengthen the sense of responsibility, work to solve the lack of decent occupation explain away, conduct problems. To establish the overall concept, eliminate departmentalism. Strict assessment and accountability, to solve the spiritual slack, nianqingpazhong, status quo, and other issues. To establish and perfect the muddle along Bureau staff conduct work regulations, standardize the behavior of personnel. 2. To strengthen the responsibility system. One is the in-depth study and implement the "Hunan provincial Party and government leading cadres Interim Provisions on the work safety of a pair of > (Hunan Office issued 2013 No. 5)," Hunan province safety supervision and management responsibilities of the provisions on the production (Hunan Zhengban made 2013 No. 4) And resolutely implement the safety production of the party with responsibility, a pair of responsibility. "Two is issued safety production administration and inspection to promote the responsibilities bear safety production supervision departments strictly and effectively assumed responsibility. The three is to establish risk self correction self reporting system for safety in production enterprises, promote the enterprises to implement the main responsibility for production safety is introduced. Four strengthen the county safety production supervision ability construction work, promote safe production responsibility to the grassroots. 3, strict accountability and target management. Adhere to the" who is in charge, who is responsible for the pipe industry must be safe, Guan Sheng production and operation must be safe, pipe business must control security "principle, the implementation of safety The production of "cure." stagnation supervision and leadership responsible system. The safety production of key towns, key enterprises and key problems, by the township government and the Department responsible for the stagnation led the lump sum, to tackle tough. To further increase the production safety index assessment, strictly implement the safety production of the "one vote veto" and the reward system, strengthen the safety incentive and restraint mechanism. (six) the implementation of the work force is not strong. The documents, meeting, long work arrangement, check and supervise the implementation of small, poor implementation of the system, the work is not effective. Some leading cadres sense of purpose, consciousness of the masses is not strong, the ruling " For the people "," the interests of the masses no matter "concept understanding is not in place. The specific work treats with the deployment, a few leading cadres complain that work is too complicated, too much responsibility, the pressure is too large, too much emphasis on the difficulty of the work, such as underground mines to avoid the disaster of" six systems "construction and construction of mechanical ventilation to file the form, forwarding arrangements work, no in-depth mining enterprises to promote the specific work, the increase in the number of files, but the effect is not good, not according to the actual situation of non coal mines in the county, to engage in" across the board ", and the quality