I am having some issues debugging my matlab program for population growth

I am creating a program to show population growth based of the equation dN/dt=aN-bN^2. I am doing something wrong though because it plot a straight line starting from the intial value of the population. Here is what I have written. Any help on pointing out where I went wrong would be much obliged.

%note: N(t)= N(int) + a*N(int)*delta_t - b*N(int)^(2)*delta_t

% Clear variable %
    clear  all

% Prompt the user %
    N_int = input('Provide a quantity for the initial number of people in a population.  ');
    a = input('Provide a value for the variable a:  ');
    b = input('Provide a value for the variable b:  ');
% Declare necesary variables %

              % time
              time_final = ???;   % I think the problem lies somewhere in declaring the variables.
              delta_t = ???;   

% Initialize variables %
      time(1)=0;
      N(1) = N_int;

% Perform calculations %

for i = 1:1:time_final

                time(i+1) = time(i) + delta_t; 
                N(i+1) = N(i) + (a*N(i)-b*N(i)^(2))*delta_t;

end

% Plot results %

          plot(time,N)
          axis([0 time_final 0 4*N_int])
          title('Population Growth Using Euler Integrator')
          xlabel('Time')
          ylabel('Population')

Answer 1

[per isakson]

I played a bit with your equation.

• converted your script to a function, cssm [attached]
• pre-allocated a couple of vectors, time and N, to improve speed
• alwaysontop and hold on
• run the function for some different input values. (I used a smaller time step.)

See alwaysontop by Elmar Tarajan

Answer 2

[Star Strider]

It seems to work, but only if you use the ‘correct’ parameters. For instance, with these, it oscillates between 5 and 10:

a = 2.5;
b = 0.3;
N_int = 10;
time_final = 50;   % I think the problem lies somewhere in declaring the variables.
delta_t = 1;

So your comment to ‘time_final’ (copied here) is correct!

Experiment with them.