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Volterra_Lotka_with_Predator_Satiation2

# Volterra_Lotka_with_Predator_Satiation2 - Volterra-Lotka...

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Volterra-Lotka with Predator Satiation By: Benjamin Horstman & Caroline Lee

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ABSTRACT: The Volterra-Lotka equations are a first order non-linear differential system. They attempt to simulate the interaction of a predator species upon an exponentially reproducing prey species: predator: ' ( ) x x y α β = - - prey: ' ( ) y y x γ δ = - (1) However, these equations are very basic and many modifications exist, for example, predator satiation . The concept behind predator satiation is that a certain number of predators can only eat so much before they become full. Thus, the rate at which the predators grow and the prey are preyed upon is not just c*x*y, where c is a growth constant. In general form: ' by x ax x c ky = - + + ' ( ) fy y d ey y x c ky = - - + (2) We attempted to determine the bifurcations caused by varying parameter k over 0 2 k y y , and holding all other variables constant. Matlab R2006a and module pplane7 were used for numeric analysis. (linearize? results?) MAIN BODY: We used the modified Volterra-Lotka system from (2) above by setting the
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Volterra_Lotka_with_Predator_Satiation2 - Volterra-Lotka...

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