% bio_phas.m
%
% b.w. bequette
% (c) 19 July 96
%
% generates phase-plane plots for the bioreactor
%
% set-up the axis limits
%
  axis([0 1.75 0 5]);
%
% stable and unstable points for substrate
% inhibition model
%
  x1u = [0.9951];
  x2u = [1.5122];
%
  x1s = [0;1.5302];
  x2s = [4;0.1746];
%
% place an 'x' on stable points
% place a 'o' on unstable points
%
  plot(x1u,x2u,'wo',x1s,x2s,'wx')
%
  hold on
%
% select different initial conditions
% x1 ranges from 0.1 to 1.5 (every 0.35)
% x2 ranges from 0 to 5 (every 1.25)
% total of 16 initial conditions
%
  x1init = [0.1 0.45 0.8 1.15 1.5 0.1 0.45 0.8 1.15 1.5];
  x2init = [ 0   0    0   0    0   5   5    5   5    5];
  x1inita = [1.5  1.5 1.5  0.1  0.1  0.1];
  x2inita = [1.25 2.5 3.75 1.25 2.5 3.75];
%
  x0 = [x1init x1inita;x2init x2inita];
%
% ncol = number of initial conditions
%
  [mrow,ncol] = size(x0);
%
% run simulations for each initial condition
%
  for i = 1:ncol;
%
    [t,x] = ode45('bio',0,30,[x0(:,i)]);
%
    plot(x(:,1),x(:,2),'w')
%
  end
%
  xlabel('x1')
  ylabel('x2')
  hold off