# The Lotka-Volterra Equations for Competition between Two Species

The Lotka-Volterra Equations for Competition between Two Species

The population dynamic of two competing species is governed by the following system of ODEs:

d

N

1

dt

r

1

N

1

K

1

N

1

N

2

K

1

d

N

2

dt

r

2

N

2

K

2

N

2

N

1

K

2

where is the population density of species (equal to 1 or 2), the intrinsic rate of species , the carrying capacity of species , and and the competition coefficients.

N

i

i

r

i

i

K

i

i

α

β

The competion may occur because (1) the two species share the same limited resources, or (2) individuals from different species have direct damaging behavior.

This Demonstration computes the population densities versus time (species 1 is shown in blue) and the snapshots show situations where one observes coexistence of both species or disappearance of one of the two species.