# Predator-Prey Model

Predator-Prey Model

This Demonstration illustrates the predator-prey model with two species, foxes and rabbits. Foxes prey on rabbits that live on vegetation. The rabbit population is and the fox population is ; both depend on time .

x

y

t

1. In the absence of foxes, the rabbit population grows at a rate proportional to its current population; thus when with .

dx/dt=ax

y=0

a>0

2. In the absence of rabbits, the foxes die out; thus when with .

dy/dt=-cy

x=0

c>0

3. The number of encounters between the species is proportional to the product of their populations. Each encounter tends to increase and decrease . Thus the growth rate of includes a term of the form and that of includes a term of the form , where and positive. The parameters , , , and are independent of . These assumptions lead to the equations:

y

x

x

-αxy

y

γxy

α

γ

a

α

c

γ

t

dx

dt

dy

dt