This module compares numerical solutions of two different models for the dynamics of the populations of two animal species, one a predator and the other its prey. Ordinary differential equations (ODEs) have applications in a wide variety of contexts, including biology and ecology. One such application is the modeling of population dynamics, in particular the interactions between predator and prey animal populations, where the populations are idealized as continuous variables. Two systems of ODEs often used to model the populations of a predator species y and its prey x are the Lotka-Volterra model,
x′ = x (α1 −
β1 y)
y′ = y (− α2 +
β2 x),
and the Leslie-Gower model,
x′ = x (α1 −
β1 y)
y′ = y (α2 −
β2 y ⁄x),
where the parameters α1 and α2 represent the natural rate of change of the prey and predator populations in isolation from each other, and the parameters β1 and β2 control the effect of interactions between the two species.
The user first selects the population model and corresponding parameter
values, the initial populations of prey and predator
Reference: Michael T. Heath, Scientific Computing, An Introductory Survey, 2nd edition, McGraw-Hill, New York, 2002. See Example 9.4 on pages 385-386 and Computer Problem 9.1 on page 418.
Developers: Evan VanderZee and Michael Heath