What are Lotka-Volterra Equations?
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order, nonlinear, 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;- t represents time; and
are positive real parameters describing the interaction of the two species.
The Lotka–Volterra system of equations is an example of a Kolmogorov model, which is a more general framework that can model the dynamics of ecological systems with predator–prey interactions, competition, disease, and mutualism.1
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