% Understanding the behaviour of systems pharmacology
% models: mathematical analysis of differential equations
% Suruchi Bakshi, Elizabeth C. de Lange, Piet H. van der Graaf, Meindert
% Danhof, and Lambertus A. Peletier


% Evaluates null clines of the original pool model for a choice of
% parameter values. Runs the original pool model for 2 different alpha 
% values in order to demonstrate the effect on movement of orbits

% Generates figure 2a in the manuscript


function y=snoeck()
global alpha;

 
t=linspace(0,5,1000);
Gammav=t;Gammau=1+0*t;
alpha=0.1;
[t1,x1]=ode23s(@feedback,[0 100],[2.5 0]);
[t2,x2]=ode23s(@feedback,[0 100],[0 2.5]);
alpha=10;
[t3,x3]=ode23s(@feedback,[0 100],[2.5 0]);
[t4,x4]=ode23s(@feedback,[0 100],[0 2.5]);
figure; set(gca,'Fontsize',18); hold on
plot(x1(:,1),x1(:,2),'r',x3(:,1),x3(:,2),'m',t,Gammav,'b',Gammau,t,'g','LineWidth',2);
xlabel('\it{u}');
ylabel('\it{v}');
axis([0 3 0.00 3]);
text(0.43,0.8,'\it{\Gamma_v}','Fontsize',24);
text(1.05,2,'\it{\Gamma_u}','Fontsize',24);
text(1.5,0.33,'\it{\alpha}=10','Fontsize',24);
text(2.4,1.7,'\it{\alpha}=0.1','Fontsize',24);
set(gca,'XTick',[0:3],'YTick',[0:3]);


 
function xdot = feedback(t,x)
global alpha;
xdot(1)= alpha*(1 - x(1));
xdot(2)= x(1) - x(2); 
xdot = xdot';