The Lotka-Volterra equations, also known as the predator-prey equations, are a pair of first order, non-linear, differential equations frequently used to describe the dynamics of biological systems in which two species interact, one a predator and one its prey. They were proposed independently by Alfred J. Lotka in 1925 and Vito Volterra in 1926. A classic model using the equations is of the population dynamics of the lynx and the snowshoe hare, popularised due to the extensive data collected on the relative populations of the ...

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• Lotka-Volterra equation - The equations
• Lotka-Volterra equation - Physical meanings of the equations
• Lotka-Volterra equation - Prey
• Lotka-Volterra equation - Predators
• Lotka-Volterra equation - Solutions to the equations
• Lotka-Volterra equation - Dynamics of the system
• Lotka-Volterra equation - Population equilibrium
• Lotka-Volterra equation - Stability of the fixed points
• Lotka-Volterra equation - Bibliography

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In the model system, the predators thrive when there are plentiful prey but, ultimately, outstrip their food supply and decline. As the predator population is low the prey population will increase again. These dynamics continue in a cycle of growth and decline. Lotka-Volterra equation - Population equilibrium. Population equilibrium occurs in the model when neither of the population levels are changing, i.e. when both of the differential equations are equal to 0. x(α − βy) = 0 See also:

Lotka-Volterra equation, Lotka-Volterra equation - The equations, Lotka-Volterra equation - Physical meanings of the equations, Lotka-Volterra equation - Prey, Lotka-Volterra equation - Predators, Lotka-Volterra equation - Solutions to the equations, Lotka-Volterra equation - Dynamics of the system, Lotka-Volterra equation - Population equilibrium, Lotka-Volterra equation - Stability of the fixed points, Lotka-Volterra equation - Bibliography

Read more here: » Lotka-Volterra equation: Encyclopedia II - Lotka-Volterra equation - Dynamics of the system

When multiplied out, the equations take a form useful for physical interpretation. Lotka-Volterra equation - Prey. The prey equation becomes: The prey are assumed to have an unlimited food supply, and to reproduce exponentially unless subject to predation; this exponential growth is represented in equation above by the term αx. The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet; this is represented above by β ...

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Lotka-Volterra equation, Lotka-Volterra equation - The equations, Lotka-Volterra equation - Physical meanings of the equations, Lotka-Volterra equation - Prey, Lotka-Volterra equation - Predators, Lotka-Volterra equation - Solutions to the equations, Lotka-Volterra equation - Dynamics of the system, Lotka-Volterra equation - Population equilibrium, Lotka-Volterra equation - Stability of the fixed points, Lotka-Volterra equation - Bibliography

Read more here: » Lotka-Volterra equation: Encyclopedia II - Lotka-Volterra equation - Physical meanings of the equations

The usual form of the equations is: where y is the number of some predator (for example, dingoes); x is the number of its prey (for example, wallabies); t represents the growth of the two populations against time; and α, β, γ and δ are parameters representing the interaction of the two species. ...

See also:

Lotka-Volterra equation, Lotka-Volterra equation - The equations, Lotka-Volterra equation - Physical meanings of the equations, Lotka-Volterra equation - Prey, Lotka-Volterra equation - Predators, Lotka-Volterra equation - Solutions to the equations, Lotka-Volterra equation - Dynamics of the system, Lotka-Volterra equation - Population equilibrium, Lotka-Volterra equation - Stability of the fixed points, Lotka-Volterra equation - Bibliography

Read more here: » Lotka-Volterra equation: Encyclopedia II - Lotka-Volterra equation - The equations