% 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 various initial
% conditions in order to plot the orbits on the phase-plane

% Generates figure 1b in the manuscript


function y=snoeck()
global u0;
 
t=linspace(0,5,1000);
Gammav=t;Gammau=1+0*t;
u0=0.4;
[t1,x1]=ode23s(@feedback,[0 100],[u0 0]);
u0=0.8;
[t2,x2]=ode23s(@feedback,[0 100],[u0 0]);
u0=1.5;
[t3,x3]=ode23s(@feedback,[0 100],[u0 0]);
u0=2;
[t4,x4]=ode23s(@feedback,[0 100],[u0 0]);
u0=2.5;
[t5,x5]=ode23s(@feedback,[0 100],[u0 0]);
u0=3;
[t6,x6]=ode23s(@feedback,[0 100],[u0 0]);
figure; set(gca,'Fontsize',18);hold on;
plot(x1(:,1),x1(:,2),'r',x2(:,1),x2(:,2),'r',x3(:,1),x3(:,2),'r',x4(:,1),x4(:,2),'r',x5(:,1),x5(:,2),'r',x6(:,1),x6(:,2),'r',t,Gammav,'b',Gammau,t,'g','LineWidth',2);
xlabel('\it{u}');
ylabel('\it{v}');
axis([0 3 0 3]);
text(0.43,0.8,'\it{\Gamma_v}','Fontsize',22);
text(1.05,2,'\it{\Gamma_u}','Fontsize',22);
text(0.55,2.4,'I','Fontsize',22);
text(1.7,2.4,'II','Fontsize',22);
text(1.7,0.3,'III','Fontsize',22);
text(0.5,0.3,'IV','Fontsize',22);
%set(gca,'XTick',[0:3],'YTick',[0:3]);

 
function xdot = feedback(t,x)
global u0;alpha=0.2;
xdot(1)= alpha*(1 - x(1));
xdot(2)= x(1) - x(2); 
xdot = xdot';