## Lotka-Voltera Model for Predator-Prey Interactions

The Lotka-Voltera model is a mathematical model that describe the interaction between two animal species, such as foxes and rabbits, one of which preys upon the other. The Lotke-Volterra model consists of the two differential equations shown below. The variables X and Y correspond to the densities of the prey and predator populations, respectively.

dX/dt = rX - aXY

dY/dt = -mY + bXY

The model also contains the following parameters:

- r = growth rate of the prey population
- a = rate at which predators kill prey
- m = death rate of predators
- b = growth rate of predators per prey killed

To graph solutions to the Lotke-Volterra model, enter values for the parameters and initial values for X and Y in the boxes below. Then click **Graph solutions**.

Paul Trow's math software.

Copyright 2010 by Paul Trow