Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear[disambiguation needed] differential equations, frequently...

a biological interaction where one organism, the predator, kills and eats another organism, its prey. It is one of a family of common feeding behaviours...

of the environment. The classic predator–prey equations are a pair of first order, non-linear, differential equations used to describe the dynamics of...

Predator–prey reversal is a biological interaction where an organism that is typically prey in the predation interaction instead acts as the predator...

for example, wolves prey mostly upon large herbivores (primary consumers), which eat plants (primary producers). The apex predator concept is applied in...

equation Hypergeometric differential equation Jimbo–Miwa–Ueno isomonodromy equations Painlevé equations Picard–Fuchs equation to describe the periods of elliptic...

cyclically around a fixed point, such as the one delineated by the predator-prey equations, would be described as persistent and resilient, but not as constant...

Prey switching is frequency-dependent predation, where the predator preferentially consumes the most common type of prey. The phenomenon has also been...

Arditi–Ginzburg equations describe ratio-dependent predator–prey dynamics. Where N is the population of a prey species and P that of a predator, the population...

(1860–1940), Italian mathematician Lotka–Volterra equations, also known as the predator–prey equations Smith–Volterra–Cantor set, a Cantor set with measure...

became known as the Malthusian growth model. The Lotka–Volterra predator-prey equations are another famous example. Population dynamics overlap with another...

For this reason, functional differential equations are more applicable than ordinary differential equations (ODE), in which future behavior only implicitly...

generalized Lotka–Volterra equations are a set of equations which are more general than either the competitive or predator–prey examples of Lotka–Volterra...

formulation. The Lotka–Volterra predator-prey equations are another famous example, as well as the alternative Arditi–Ginzburg equations. Simplified population...

predicted by the Lotka-Volterra equation, with the peaks in prey abundance shifted slightly to the left of the peaks of the predator densities. Huffaker's experiments...

differential equations within biology is Lotka-Volterra equations are prey-predator equations A governing equation may also be a state equation, an equation describing...

It is a specialist predator and depends heavily on the snowshoe hare (Lepus americanus) for food. This leads to a prey-predator cycle, as the Canada...

terrestrial vertebrate to develop the curved, serrated teeth that enable a predator to eat prey much larger than itself." While amphibians continued to feed on fish...

formulation. The Lotka–Volterra predator-prey equations are another famous example, as well as the alternative Arditi–Ginzburg equations. When describing growth...

the animals already living in the environment. Predator-prey dynamics – Equations modelling predator–prey cyclesPages displaying short descriptions of redirect...

is a predator that prevents a particular herbivorous species from eliminating dominant plant species. If prey numbers are low, keystone predators can be...

other, or symmetrical, in which both species prey upon each other. Because the dominant intraguild predator gains the dual benefits of feeding and eliminating...

equation models the efficiency at which predators consume prey. The model predicts that as the number of prey increases, the amount of time predators...

set of first-order, nonlinear, differential equations, which are frequently used to describe predator–prey interactions, can be modified to account for...

experiments in which prey densities are artificially manipulated, but is rare in nature. Ecosystem model Lotka–Volterra equations Predator satiation Holling...

between modelled and real predator–prey interactions. Rosenzweig used ordinary differential equation models to describe changes in prey populations. Enrichment...

populations of both predator and the prey. In 1925, the American mathematician Alfred J. Lotka developed simple equations for predator–prey interactions in...

experiments with predatory and herbivorous mite species to investigate predator–prey population dynamics. In these experiments, he created model universes...

become circular. Forage fish are small fish which are preyed on by larger predators for food. Predators include other larger fish, seabirds and marine mammals...

Clements, was important in early plant ecology. Alfred Lotka's predator-prey equations, G. Evelyn Hutchinson's studies of the biogeography and biogeochemical...