Discrete Population Growth Model Plot

Use the detailed, discrete model for population growth that follows a variation of the logistic law:

with . Calculate the population after iterations and present a graph of the population evolution."

Let me know if you'd like assistance calculating or graphing the population evolution.

I've written a MATLAB script to simulate a discrete population growth model that follows a variation of the logistic law. My objective is to calculate and visualize the population evolution over time given specific parameters. Here's the code I currently have:

%parameters
N=150;
r=3;
q=0.05;
l=0.1; 
H=1;
a=1.5;
t=1;
P(1)=1;

for i=2:N;
P(i)=r*P(i-1)-q*P(i-1)^2-l*(H+P(i-1)^a);
t=t+1;
end;

% Plot population evolution
figure;
plot(P)
P(N)

ans = 29.1358

xlabel('i')
ylabel('P(i)')
title('Population Evolution Over Time');
grid on;

Although this code works, I'd like to optimize it or make improvements. Are there ways to enhance the efficiency or clarity of the code? Any suggestions for improving the logic, structure, or visual presentation would also be greatly appreciated.

Thanks in advance for your help!

[Torsten]

Maybe it's interesting to additionally compute steady-state for P:

r=3;
q=0.05;
l=0.1; 
H=1;
a=1.5;
fun = @(P)P-(r*P-q*P^2-l*(H+P^a));
fzero(fun,30)

ans = 29.1358