MathLiveLotka–Volterra equations
A pair of coupled nonlinear differential equations describing how the populations of a predator and its prey change over time. The prey population x grows on its own and is eaten at a rate proportional to the encounters with predators, while the predator population y grows from eating prey and declines otherwise.
\begin{aligned}\frac{\mathrm dx}{\mathrm dt}&=\alpha x-\beta xy\\\frac{\mathrm dy}{\mathrm dt}&=\delta xy-\gamma y\end{aligned}What the symbols mean
| prey population density | |
| predator population density | |
| time | |
| prey growth rate | |
| rate at which predators consume prey | |
| rate at which consumed prey converts into predator growth | |
| predator death rate |
About this formula
- FieldBiology and medicine
- TopicPopulation dynamics
- LevelUniversity
- Also calledLotka-Volterra equation, predator-prey equations, predator prey model, Volterra principle, predator prey equation, Lotka Volterra model
- SourceWikidata Q150052
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