bvp_hom.m

计算动力学系统的分岔图

function f = BVP_Hom(x,YS,YU,p)
global homds 

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

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

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

% -----------
% Ricatti equations
f(end+1:end+homds.ns*homds.nu,1) = Hom_RicattiEval(x0,p,1,YU);

f(end+1:end+homds.nu*homds.ns,1) = Hom_RicattiEval(x0,p,0,YS);

% -----------
% Last and first vectors along stable and unstable eigenspaces
Q0U = homds.Q0;
Q1S = homds.Q1;

if homds.nu
    Q1U = Q0U * [-YU'; eye(size(YU,1))];
    
    for i=1:homds.ns      
        f(end+1,1) = (ups(:,2) - ups(:,1))' * Q1U(:,end-i+1);
    end
end

if homds.ns
    Q1S = Q1S * [-YS'; eye(size(YS,1))];
    for i=1:homds.nu
        f(end+1,1) = (ups(:,end) - ups(:,1))' * Q1S(:,end-i+1);
    end
end

%f,pause
%eps0=homds.eps0;
%eps1=homds.eps1;
%f(end+1,1) = norm(ups(:,2) - x0) - eps0;
%f(end+1,1) = norm(ups(:,end) - x0) - eps1;
% -----------

%size(f),pause
%f,
%pause