init_he_he.asv

计算动力学系统的分岔图

function [x,v] = init_HE_HE(mapfile, C, p,ap, eps0,eps1,J)

global hetds cds
% 
[n1,n2]=size(C);% X=[x1,..., xn2], xi,i=1,...,n2 are  mesh points 
hetds.nphase=n1;
hetds.npoints=n2;
hetds.niteration=J;
hetds.sizep = size(p,1);

% initialize hetds
func_handles = feval(mapfile);
symord = 1; 
symordp = 0;
%
cds.curve = @heteroclinic;
cds.symhess = 0;%1
cds.symjac  = 1;%1 
curvehandles = feval(cds.curve);
cds.curve_func = curvehandles{1};
cds.curve_options = curvehandles{3};
cds.curve_jacobian = curvehandles{4};%
%cds.curve_hessians = curvehandles{5};
%cds.curve_testf = curvehandles{6};
cds.options = feval(cds.curve_options);
cds.options = contset(cds.options,'Increment',1e-5);
%

if     ~isempty(func_handles{9}),   symord = 5; 
elseif ~isempty(func_handles{8}),   symord = 4; 
elseif ~isempty(func_handles{7}),   symord = 3; 
elseif ~isempty(func_handles{5}),   symord = 2; 
elseif ~isempty(func_handles{3}),   symord = 1; 
end
if     ~isempty(func_handles{6}),   symordp = 2; 
elseif ~isempty(func_handles{4}),   symordp = 1; 
end
if isempty(cds)
    cds.options = contset();
end

cds.options = contset(cds.options, 'SymDerivative', symord);
cds.options = contset(cds.options, 'SymDerivativeP', symordp);

hetds.mapfile = mapfile;
hetds.func = func_handles{2};
hetds.Jacobian  = func_handles{3};
hetds.JacobianP = func_handles{4};
hetds.Hessians  = func_handles{5};
hetds.HessiansP = func_handles{6};
hetds.Der3 = func_handles{7};
hetds.Der4 = func_handles{8};
hetds.Der5 = func_handles{9};
%
siz = size(func_handles,2);
if siz > 9
    j=1;
    for k=10:siz
        hetds.user{j}= func_handles{k};
        j=j+1;
    end
else hetds.user=[];end
%hetds.nphase = oldhetds.nphase;
% hetds.x0 = oldhetds.x0;
%hetds.x0 = x(oldhetds.ncoords+1:oldhetds.ncoords+oldhetds.nphase);
hetds.ActiveParams = ap;
hetds.P0 = p;
hetds.eps0 = eps0;
hetds.eps1 = eps1;
%
x0=C(:,1);x1=C(:,end); % x0 and x1 are fixed points
A0 = hetjac(x0,num2cell(p),J);
D0 = eig(A0);
%hetds.nu is dimension of the unstable invariant  space corresponds to D0

%hetds.nu=size(find(abs(D0)>1),1);
hetds.nu= sum(abs(D0)>1);
if (hetds.nu == hetds.nphase)
    if min(abs(D0)-1) < 1e-2
        hetds.nu = hetds.nu -1;
    end
end
if (hetds.nu == 0)
    if min(abs(D0)) < 1e-2
        hetds.nu = hetds.nu +1;
    end
end

A1 = hetjac(x1,num2cell(p),J);
D1 = eig(A1);
%hetds.ns is dimension of the stable invariant  space corresponds to D1

%hetds.ns = size(find(abs(D1)<1),1);hetds.ns,66,pause 
hetds.ns = sum(abs(D1)<1);
if (hetds.ns == hetds.nphase)
    if min(abs(D1)-1) < 1e-2
        hetds.ns = hetds.ns -1;
    end
end
if (hetds.ns == 0)
    if min(abs(D1)) < 1e-2
        hetds.ns = hetds.ns +1;
    end
end
%  YS and YU, initialized to 0
x=x0;
for i=2:hetds.npoints
    x(end+1:end+hetds.nphase,1)=C(:,i);
end

hetds.YU=zeros(hetds.nphase-hetds.nu,hetds.nu);
for i=1:hetds.nu
  %x(end+1:end+hetds.nphase-hetds.nu,1)=YU(:,i);
  x=[x;zeros(hetds.nphase-hetds.nu,1)];
end
% 
hetds.YS=zeros(hetds.nphase-hetds.ns,hetds.ns);
for i=1:hetds.ns
 %x(end+1:end+hetds.nphase-hetds.ns,1)=YS(:,i);
 x=[x;zeros(hetds.nphase-hetds.ns,1)];
end
x(end+1,1)=eps0;
x(end+1,1)=eps1;
x(end+1,1)=p(ap);  %x=(x1,..,xN,YU,YS,eps0,eps1,ap)^T
v = [];
cds.ndim = length(x);

% ASSIGN SOME VALUES TO HETEROCLINIC FIELDS
% ---------------------------------------

%hetds.YU = zeros(hetds.nphase,hetds.nu);
%hetds.YS = zeros(hetds.nphase,hetds.ns);
% Third parameter = unstable_flag, 
% 1 if we want the unstable space, 0 if we want the stable one

[QU, eigvlU, dimU] = computeBase(A0,1,hetds.nu);
[QS, eigvlS, dimS] = computeBase(A1,0,hetds.ns);
hetds.Q0 = QU;
hetds.Q1 = QS;
x
%size(x),pause