Predator-Prey Systems and Lotka_Volterra Equation

> restart;with(DEtools):

Plot of the direction field for the Lotka-Volterra system in Example 1, p. 547.

> dfieldplot([diff(R(t),t)=0.08*R(t)-0.001*R(t)*W(t),diff(W(t),t)=-0.02*W(t)+0.00002*R(t)*W(t)], \
[R(t),W(t)],t=0..20,R=0..3010,W=0..150,arrows=MEDIUM,title=`Lotka-Volterra model - Example 1, p. 547`,\
color=[-0.02*W(t)+0.00002*R(t)*W(t),0.08*R(t)-0.001*R(t)*W(t),.1]);

[Maple Plot]

A Phase Portrait of the same system.

> phaseportrait([diff(R(t),t)=0.08*R(t)-0.001*R(t)*W(t),diff(W(t),t)=-0.02*W(t)+0.00002*R(t)*W(t)], \
[R(t),W(t)],t=0..200,[[R(0)=1000,W(0)=40],[R(0)=1000,W(0)=55],[R(0)=1000,W(0)=70]],stepsize=.05,R=0..3000,W=0..150,arrows=MEDIUM,title=`Predator-Prey System - Phase Portrait`, color=[-0.02*W(t)+0.00002*R(t)*W(t),0.08*R(t)-0.001*R(t)*W(t),.1]);

[Maple Plot]

>