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

biological interaction in which 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...

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...

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

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

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...

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

predator-prey interactions and population dynamics. The model was an improvement over earlier predator-prey models, notably the Lotka–Volterra equations, by...

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...

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

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...

Lotka-Volterra equations for modeling a predator-prey eco-system) or in a more realistic manner by a discrete event simulation model (in a predator-prey eco-system...

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...

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

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

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

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

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

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

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

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

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

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

employed to describe how populations depend on each other, for example in predator-prey systems, or relationships between herbivores and their food source....

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

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

introduced in the differential equations of the Kolmogorov predator–prey model. It generalizes the linear case of predator–prey interaction firstly described...

many mathematical equations, including self-oscillatory systems, excitable systems and reaction–diffusion–advection systems. Equations of these types are...