Here we were looking at solutions of the predator-prey problem:

           dx/dt = x - 4*x*y
           dy/dt = -y + 2*x*y

>> help sys_runge_kutta_2

  the program takes the intial data x_0 and y_0 at the initial time t_0 and 
  computes up to time t_final using n timesteps.  It creates
  three vectors, t, x and y, which you can then plot against each other
  plot(x,y), hold on, plot(x(1),y(1),'o')
 
  [t,x,y] = sys_runge_kutta_2(x_0,y_0,t_0,t_final,n)

>> x_0 = 1; y_0 = 1; t_0 = 0; t_final = 30; n = 1000;
>> [t,x,y] = sys_runge_kutta_2(x_0,y_0,t_0,t_final,n);
>> figure(2)

We find that the solution appears to go in a counter-clockwise
orbit around the fixed point (1/2,1/4):
>> plot(x,y)
>> figure(1)
We find that the solutions appear to be periodic in time, with
the expected behavior when viewed in terms of predator and prey.
>> plot(t,x), hold on; plot(t,y,'r-');

Next...  consider
           dx/dt = a*x - b*x*y
           dy/dt = -c*y + d*x*y
and play around with the parameters a,b,c, and d.  Also, fix
the parameters and play around with the initial data.

>> diary off