% 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


% Generates figure 7b in the manuscript

clear all
clc
close all

% Select the parameter to vary
beta = 0.5:0.1:1.5;
% Select parameter(s) to fix
gamma = 1;

% bifurcation parameter
bp = beta./gamma;

% Evaluate both steady states as functions of the bifurcation parameters
v_ss_1 = ones(1,length(bp));
v_ss_2 = ones(1,length(bp)) + beta - gamma;

% get index at which the bifurcation parameter is at the critical value
ind = find(bp'==1);

% Plot the bifurcation diagram - Figure 7b in the manuscript
figure;
set(gca,'Fontsize',15)
plot(bp(1:ind), v_ss_1(1:ind)','b','Linewidth',2);
hold on
plot(bp(ind:end), v_ss_1(ind:end),'b--','Linewidth',2);
plot(bp(1:ind), v_ss_2(1:ind),'r--','Linewidth',2);
hold on
plot(bp(ind:end), v_ss_2(ind:end),'r','Linewidth',2);
%xlabel('\beta/\gamma')
xlabel('\lambda')
ylabel('steady states of \it{v}')
legend('\it{v_{0}} - \rm{stable}','\it{v_{0}} - \rm{unstable}','\it{v_{1}} - \rm{unstable}','\it{v_{1}} - \rm{stable}')
xlim([0.5 1.5]); ylim([0.5 1.5])

% Plot the bifurcation diagram without the stability properties
figure;
set(gca,'Fontsize',15)
hold on
plot(bp, v_ss_1','b','Linewidth',2);
plot(bp, v_ss_2','r','Linewidth',2);
%xlabel('\beta/\gamma')
xlabel('\lambda')
ylabel('steady states of \it{v}')
legend('\it{v_{0}}','\it{v_{1}}')
xlim([0.5 1.5]); ylim([0.5 1.5])