Defining the Model

Next we study solutions of the Lotka-Volterra system (similar to the system discussed at the bottom of page 144 in the text). In this model the prey is assumed to grow logistically in the absence of any predators. Can you see how the rate equations have been changed from the original L-V model to incorporate this assumption? This time represents the rabbit population and represents 100 times the fox population. We are going to work with three different initial conditions.

> rate_eqn1 := diff(R(t),t) = (0.1)*R(t)-.00001*R(t)^2-(0.005)*R(t)*(1/100)*F(t) ;

> rate_eqn2 := diff(F(t),t) = (0.00004)*R(t)*F(t)-(0.04)*F(t) ;

> MODEL := { rate_eqn1, rate_eqn2 };

> vars := { R(t), F(t) } ;

> init1 := [R(0)=2000,F(0)= 500];

> init2 := [R(0)=2000,F(0)=1000];

> init3 := [R(0)=2000,F(0)=5000];

> domain := t = 0 .. 380;