Time for action - using lsode for numerical integration

1. 1. Since we have an autonomous system, we can simply use the function given in Code Listing 5.5 as input to lsode. First,we specify the time vector array to contain 200 elements equally spaced from 0 to 50 as well as the initial condition:

octave:26>global_b = 1; t = linespace(0,50,200); init = [0.4 0.2];

1. 2. Next we call lsode to obtain a numerical solution to the Sel'kov model:

octave:27> x = lsode("selkov", init, t);

1. 3. Now, the output variable x contains the solutions to x1 and x2 in a column-wise manner, meaning column one is the solution for x1 and column two for x2. We can then plot the columns versus the time vector array, for example:

2See http://www.netlib.org/alliant/ode/prog/lsode.f

octave:28> plot(t, x(:,1), "-r", "linewidth", 5, t, x(:,2), "-b", "linewidth", 5);

1. 4. The result (or something close to it, depending on your plotting program) is shown in the left-hand side window in the figure below.

   If we repeat Commands...