write a script file for dx/dt=rx(1-x/k) in matlab

To write a script file for the given differential equation dx/dt = rx(1-x/k) in Matlab, we can use the built-in ODE solvers to simulate the behavior of this differential equation. The following code can be used in Matlab script file:


main.m
% Declare parameters
r = 0.8;  % growth rate
k = 100;  % carrying capacity

% Define the differential equation
dxdt = @(t,x) r*x*(1-x/k);

% Set initial conditions
x0 = 5;  % initial population

% Set up time interval for simulation
tspan = [0 200];  % start and end time

% Use built-in ODE solver to simulate the differential equation
[t,x] = ode45(dxdt, tspan, x0);

% Plot the results
plot(t,x);
xlabel('Time');
ylabel('Population');
title('Population growth model');
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Here, we first declare the growth rate r and the carrying capacity k as parameters. Then, we define the differential equation using an anonymous function dxdt that takes in the time t and the current population x.

We set the initial population x0 and the time interval tspan for simulation. Finally, we use the ode45 solver to simulate the differential equation and obtain the time and population vectors t and x.

The plot function is used to visualize the results. The resulting plot shows how the population grows over time, starting from an initial population of x0.