title: plot of 3 competing species with diffusion
body: <p>I want to make a code for a model of competing three species with diffusion to get plots (  2d plot u, v, w against time ) My model is</p>
  
  <pre><code>u'=d1u_xx+(r1-a1u-b1v-c1w)u
  v'=d2v_xx+(r2-a2u-b2v-c2w)v
  w'=d3w_xx+(r3-a3u-b3v-c3w)w
  where d1=d2=d3=1;
  r1=1.5; r2=2.65; r3=3.45;
  a1=0.1; b1=0.3; c1=0.01; b2=0.2;
  a2=0.3; c2=0.2; c3=0.2; a3=0.01; b3=0.1.
  </code></pre>
  
  <p>I did the code for this model without diffusion as follow</p>
  
  <pre><code>% Define diff. equations, time span and initial conditions, e.g.
  tspan = [0 20];
  y0 = [0.2 0.2 0.2];
  
  r1=1.5;     r2=2.65;    r3=3.45;
  a1=0.1;     a2=0.3;     a3=0.01; 
  b1=0.3;     b2=0.2;     b3=0.1;
  c1=0.01;    c2=0.2;     c3=0.2; 
  
  dy = @(t,y) [
  (r1-a1*y(1)-b1*y(2)-c1*y(3))*y(1);
  (r2-a2*y(1)-b2*y(2)-c2*y(3))*y(2);
  (r3-a3*y(1)-b3*y(2)-c3*y(3))*y(3)];
  
  % Solve differential equations
  [t,y] = ode45(dy, tspan, y0);
   % Plot all species against time
  figure(1)
  plot(t,y)
  </code></pre>
  
  <p>Resulting in following figure:</p>
  
  <p><a href="https://i.stack.imgur.com/ClXr5.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/ClXr5.png" alt="enter image description here"></a></p>
  
  <p>how to do it with diffusion like in  <a href="https://www.projecteuclid.org/download/pdf_1/euclid.hmj/1372180511" rel="nofollow noreferrer">this paper</a> figure 10u, v, w </p>