# M145L.W99, Week 2
# by ralph abraham, 09 january 1999
# file: popul02, this is a MapleVr5 worksheet 
# 
# we follow Strogatz sec 2.3, p. 21
# see also MapleV Learning Guide sec 6.2, p. 220
# 
# This is the population dynamics model of VerHulst, 1834, based
# on the logistic function. Experiment with changes in the parameters.
# Define the vectorfield
> r := 3.6:
> K := 1.0:
> expr := r*n*(1-n/K):
> f := unapply( expr, n);

                 f := n -> 3.6 n (1 - 1.000000000 n)

> plot( f(n), n=-0..1);

# Setup initial conditions
> myvector := subs({n=N(t)}, expr):
> eq := diff(N(t),t)=myvector:
> ini1 := N(0) = 2.0:
> ini2 := N(0) = 1.0:
> ini3 := N(0) = 0.1:
# Plot the direction field and trajectories
> with(DEtools):
> DEplot( eq, N, t=0..1, [ [ini1] , [ini2] , [ini3] ] );

# This is the end of file: popu02