Lotka–Volterra Equations

Equations modelling predator–prey cycles This article is about the predator-prey equations. For the competition equations, see Competitive Lotka–Volterra equations The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, 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: d x d t = α x − β x y , d y d t = − γ y + δ x y , {\displaystyle {\begin{aligned}{\frac {dx}{dt}}&=\alpha x-\beta xy,\\{\frac {dy}{dt}}&=-\gamma y+\delta xy,\end{aligned}}} where the variable x is the population density of prey (for example, the number of rabbits per square kilometre); is the population density of prey (for example, the number of rabbits per square kilometre); the variable y is the population density of some predator (for example, the number of foxes per squa ... Read full article.