Lotka–Volterra equations

A pair of nonlinear differential equations describing changes in interacting populations, classically a predator and its prey. Their simplest form produces repeating cycles under idealized assumptions.

Predator–prey model: A mathematical representation of interactions in which one population consumes another. The equations are the classic two-species example of this broader modeling approach.
Exponential growth: Growth in which a quantity's rate of increase is proportional to its current size. The prey equation reduces to exponential growth when predators are absent.
Alfred J. Lotka: An American mathematician and physical chemist who developed mathematical models of biological populations. He presented a predator–prey system in his 1925 book Elements of Physical Biology.
Rosenzweig–MacArthur model: A predator–prey model incorporating prey growth limits and a saturating predator response. Its added mechanisms can produce stable coexistence where the classical equations predict neutral cycles.
Population dynamics: The study of how and why populations change in size and structure over time. The equations provide a foundational model for interactions between changing populations.
Ordinary differential equation: An equation relating a function of one variable to its derivatives. Each population's rate of change is specified as a function of current population sizes.
Mass-action kinetics: A modeling rule in which interaction rates depend on the product of interacting quantities. The predation term assumes encounters increase with both prey and predator abundance.
Vito Volterra: An Italian mathematician whose work included mathematical models of biological populations. He independently formulated the equations while studying fluctuations in Adriatic fishing catches.
Holling type II functional response: A saturating relationship between prey density and predator consumption caused by handling time. It replaces the classical model's indefinitely increasing, linear predation rate.
Fisheries science: The study and management of fish populations and aquatic ecosystems. Volterra applied the model's principles to explain changes in fish catches under fishing pressure.

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