bvp_het.m

计算动力学系统的分岔图

function f = BVP_Het(x,YS,YU,p)
global hetds 

% extract ups,  [x0,x1,...,xn]

ups = reshape(x,hetds.nphase,hetds.npoints);
p = num2cell(p);

% -----------
% Fixed points conditions
J=hetds.niteration;
x0=ups(:,1);
xx=x0;
for i=1:J
xx=feval(hetds.func,0,xx,p{:}); %f^i(x0)-x0
end 
f(1:hetds.nphase,1)=xx-x0;
for i=2:hetds.npoints-2
     xx=ups(:,i);
   for k=1:J
     xx=feval(hetds.func,0,xx,p{:});
   end    
    f(end+1:end+hetds.nphase,1)=xx-ups(:,i+1);;%f^i(xi)-xi+1
end
 x1=ups(:,end);xx=x1;
for i=1:J
  xx=feval(hetds.func,0,xx,p{:}); 
end 
  f(end+1:end+hetds.nphase,1)=xx-x1;%f^i(x1)-x1

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

% Ricatti equations

f(end+1:end+hetds.ns*hetds.nu,1) = Het_RicattiEval(x0,p,1,YU);
%Y_u output of RicattiEval is a (n-nu)*nu matrix
f(end+1:end+hetds.nu*hetds.ns,1) = Het_RicattiEval(x1,p,0,YS);
%Y_s output of RicattiEval is a (n-ns)*ns matrix

% -----------
% Last and first vectors along stable and unstable eigenspaces
Q0U = hetds.Q0;
Q1S = hetds.Q1;
if hetds.nu
    Q1U = Q0U * [-YU'; eye(size(YU,1))];   
    for i=1:hetds.ns    
    
        f(end+1,1) = (ups(:,2) - ups(:,1))' * Q1U(:,end-i+1);%ups(:,1),ups(:,2),Q1U,pause
       
    end
end
if hetds.ns
    Q1S = Q1S * [-YS'; eye(size(YS,1))];
    for i=1:hetds.nu 
   
        f(end+1,1) = (ups(:,end-1) - ups(:,end))' * Q1S(:,end-i+1);
        
    end
end




% global hetds
% hetds.Q0,
% hetds.Q1
% norm(f),pause

%f,pause,norm(f),pause
%rf=size(f),pause
% -----------
%f,pause
%  NF=norm(f),pause
%normf=norm(f),pause