# M145L.W99, Week 2
# by ralph abraham, 09 january 1999
# file: volt02, this is a MapleVr5 worksheet 
# 
# we follow Strogatz Ch. 6, p. 189
# see also MapleV Learning Guide sec 6.2, p. 232
# 
# This is the population dynamics model of Volterra-Lotka, 1924, based
# on the logistic function. Experiment with changes in the parameters.
# Define the vectorfield
> r := 0.5:
> xdotexpr := x*(1-y):
> ydotexpr := r*y*(x-1):
# Setup initial conditions
> myvector1 := subs({x=X(t), y=Y(t)}, xdotexpr):
> myvector2 := subs({x=X(t), y=Y(t)}, ydotexpr):
> eq1 := diff(X(t),t)=myvector1:
> eq2 := diff(Y(t),t)=myvector2:
> ini := X(0) = 0.9, Y(0) = 0.9:
# Plot the direction field and trajectories
> sol1 := dsolve( {eq1, eq2, ini}, {X(t),Y(t)}, type=numeric );

                   sol1 := proc(rkf45_x)  ...  end

> with(plots):
> odeplot( sol1, [X(t), Y(t)], 0..10, labels=["x","y"] );

# This is the end of file: volt01