%ESB 2/19/08
clear all
% Make quiver plot for Michaelis-Mentin equations

%First, in orig. (s,c) variables

clist=0:.03:.2;
slist=0:.1:1;

[cmatrix,smatrix]=meshgrid(clist,slist);

dcdt_matrix=zeros(size(cmatrix));
dsdt_matrix=zeros(size(cmatrix));


for i=1:length(slist)
    for j=1:length(clist)
    dxdt=michaelis_mentin_odefun(0,[cmatrix(i,j);smatrix(i,j)]);
    dcdt_matrix(i,j)=dxdt(1);
    dsdt_matrix(i,j)=dxdt(2);
    end
end


figure
set(gca,'FontSize',16)
quiver(cmatrix,smatrix,dcdt_matrix,dsdt_matrix,.5,'LineWidth',1)
xlabel('c','FontSize',20);ylabel('s','FontSize',20)

pause
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Next, in rescaled variables

vlist=0:.1:1;
slist=0:.1:1;

[vmatrix,smatrix]=meshgrid(vlist,slist);

dvdt_matrix=zeros(size(vmatrix));
dsdt_matrix=zeros(size(vmatrix));

for i=1:length(slist)
    for j=1:length(vlist)
    dxdt=michaelis_mentin_rescaled_odefun(0,[vmatrix(i,j);smatrix(i,j)]);
    dvdt_matrix(i,j)=dxdt(1);
    dsdt_matrix(i,j)=dxdt(2);
    end
end


figure
set(gca,'FontSize',16)
quiver(vmatrix,smatrix,dvdt_matrix,dsdt_matrix,'LineWidth',1)
xlabel('v','FontSize',20);ylabel('s','FontSize',20)