plot a logistical population growth model with different value outputs in matlab

To plot a logistical population growth model with multiple value outputs in Matlab, you can follow these steps:

1. Define the variables:

   • r = the intrinsic growth rate (dN/dt) of the population
   • K = the carrying capacity of the population
   • N0 = the initial population size
   • t = the time frame for the population growth

2. Write the logistic function formula:

   main.m
   N = K ./ (1 + ((K-N0)/N0)*exp(-r*t))
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3. Use the plot() function to plot the population size N as a function of time t. You can also include multiple output curves by specifying different input values for the variables r, K and N0.

Here's an example code snippet:

main.m
% Define variables
r1 = 0.5;  % intrinsic growth rate for first population
r2 = 0.8;  % intrinsic growth rate for second population
K = 1000;  % carrying capacity
N0 = 50;   % initial population size
t = 0:50;  % time frame for population growth

% Logistic model equation
N1 = K ./ (1 + ((K-N0)/N0)*exp(-r1*t));
N2 = K ./ (1 + ((K-N0)/N0)*exp(-r2*t));

% Plot the results
plot(t, N1, '-b', t, N2, '-r')
xlabel('Time')
ylabel('Population Size')
title('Logistical Population Growth Model')
legend('Population 1', 'Population 2')
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This will produce a plot with two curves representing the growth of two populations with different intrinsic growth rates (r1 and r2) but same carrying capacity and initial population size. You can adjust the variables as needed to explore different scenarios.