# Competing Species Model with Two Species

Competing Species Model with Two Species

This Demonstration illustrates the competing species model with two species, foxes and hawks. Foxes and hawks both prey on rabbits, of which there is a limited supply. The fox population is and the hawk population is ; both depend on time .

x

y

t

1. In the absence of hawks, the foxes would grow logistically; thus =x(-x) when , where is the growth rate and is the carrying capacity for the fox population.

dx

dt

ϵ

1

σ

1

y=0

ϵ

1

ϵ

1

σ

1

2. In the absence of foxes, the hawks would grow logistically; thus =y(-y) when , where is the growth rate and is the carrying capacity for the hawk population.

dy

dt

ϵ

2

σ

2

x=0

ϵ

2

ϵ

2

σ

2

3. When both foxes and hawks are present, a sufficiently large number in either population will cause a decrease in the growth of both populations. Thus the model for competing species requires additional parameters and that determine the effect of large populations:

α

1

α

2

dx

dt

ϵ

1

σ

1

α

1

dy

dt

ϵ

2

σ

2

α

2