predator-prey interactions

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.