ode45 simulation for a logistical population model in matlab

The following code implements a logistical population model using ode45 solver in MATLAB.

main.m
% Define the parameters
r = 0.5;        % growth rate
K = 100;        % carrying capacity
y0 = 10;        % initial population

% Create a function that calculates the differential equation
f = @(t,y) r*y*(1 - y/K);

% Set the time span
tspan = [0 50];

% Solve the differential equation using ode45 solver
[t,y] = ode45(f, tspan, y0);

% Plot the results
plot(t,y)
xlabel('time')
ylabel('population')
title('Logistic Population Model')
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In this code, we first define the parameters of the logistical population model: growth rate r, carrying capacity K, and initial population y0. We then create a function f to calculate the differential equation based on the model. Next, we set the time span tspan for which we wish to simulate the model. We then use the ode45 solver to calculate the solution to the differential equation, and store the results in two variables t and y. Finally, we plot the results using plot function.