Phase Portrait

Next we plot the rabbit and fox populations against one another in what is called a PHASE PORTRAIT. We do this for three different initial conditions. ***Can you identify which curve goes with which initial condition? How is the independent variable t showing up in these pictures? (Hint: try it again with time interval t = 0 .. 20.) ***

> domain := t = 0 .. 160;

> DEplot( MODEL, vars, domain, [ init1, init2, init3 ], stepsize=0.5, scene=[R,F],

> title=`Rabbits vs. 60 * Foxes for t = 0 .. 160`, linecolor = [ cyan, maroon, black], arrows= MEDIUM );

>

Identify the initial point on each solution curve.

How long does it take for the solution to pass through one period? (Adjust the period to see when each curve completes a single cycle.)

Does the period depend on the initial condition?