MATLAB Plot of Solutions and Directional Field

Question

I'm trying to plot solutions along with the directional field as in the image given below, of the constant harvesting model given by

dP/dt = r*P(1 - (P/M)) - h , P(0) =p0 , where r = 0.8, M = 8000 and h = 0 in this particular case.

I attempted using the following code, which does not result in something as in the image 1. I would appreciate your help with making the graph looks like as in the image 1.

Image 1(Required graph): drive[DOT]google.com/file/d/1WPREaQrGLi_cGrXevtN5ajMq1QR4acGI/view?usp=sharing

Image 2(The result I got with my code): drive.google[DOT]com/file/d/1QkDFIsTO0UzZfRCpBhfZtiPnpqlWPxL0/view?usp=sharing

I'm using MATLAB online free version

Answer 1

SET parameters r = 0.8, M = 8000, h = 0

DEFINE time range t from 0 to 20

DEFINE population range P from 0 to 9000

CREATE a grid of points (T, Pgrid) using meshgrid over t and P

FOR each point in the grid:

COMPUTE slope dPdt = r * Pgrid * (1 - Pgrid/M) - h

NORMALIZE slopes:

SET dt = 1 for all points

COMPUTE magnitude = sqrt(dt^2 + dPdt^2)

DIVIDE dt and dPdt by magnitude

PLOT the slope field using quiver(T, Pgrid, dt, dPdt)

FOR each initial population value p0 in [100, 1000, 4000, 7000, 8500]:

SOLVE the ODE dP/dt = r*P*(1 - P/M) - h from t=0 to t=20 using ode solver

PLOT the solution curve

LABEL axes and add title

DISPLAY gridlines