The
Lotka–Volterra equations, also known as the
predator–prey equations, are a pair of first-order,
non-linear,
differential equations frequently used to describe the
dynamics of
biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:
where
- x is the number of prey (for example, rabbits);
- y is the number of some predator (for example, foxes);
- and represent the growth rates of the two populations over time;
- represents time; and
- are positive real parameters describing the interaction of the two species.