pred-prey-satiation

Pred-prey-satiation - rates of growth of the two species and the carrying capacity of the prey population/Set the parameters a =.5 d = 1 e = 1 b =

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Sheet1 Page 1 Predator-Prey Model with Satiation: Bifurcation study Equations for x-predator, y -prey x' = -a*x + (b*y/(c + k*y))*x y' = (d - e*y)*y - (f*y/(c + k*y))*x Description of the equations: This model for predator-prey popu- lations incorporates predator satiation. The consumption rate of the predator levels-off as the prey population increases in size. As the prey population increases in size, the predators have a limited capacity to reduce the numbers of prey. This can lead to oscillations in predator-prey popu- lation sizes that grow in time, to stable limit cycles, and other effects. Parameters b, c, f and k influence the per-capita predation rate of the predators on the prey. They determine the interaction between the two species. Parameters a, e and f are the usual parameters that determine the intrinsic
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Unformatted text preview: rates of growth of the two species, and the carrying capacity of the prey population. //Set the parameters: a = .5 d = 1 e = 1 b = 1 c = .3 f = 1 Experiment with k vary from k = 0 to 2 with 20 values. Use common IC (Iinitial condition) x = 0.25, y = 0.5 for all solutions. You will see the solutions change their behavior as k passes through certain critical bifurcation values. The goal of the project is 1) determine (approximately) the bifurcation values k 2) compare your conclusions with the analysis of equilibria (could "linearized system at equilibria" predict the non-linear bifurcations?) 3) describe the qualitative Sheet1 Page 2 changes in the behavior of solutions and discuss their effect on coexistence of predator - prey....
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This note was uploaded on 05/09/2008 for the course MATH 224 taught by Professor Hahn during the Spring '07 term at Case Western.

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Pred-prey-satiation - rates of growth of the two species and the carrying capacity of the prey population/Set the parameters a =.5 d = 1 e = 1 b =

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