M334Lec39

M334Lec39 - Math 334 Lecture#39 9.5 Predator-Prey...

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Unformatted text preview: Math 334 Lecture #39 § 9.5: Predator-Prey Equations Outcome A: Apply Phase Plane Analysis to Predator-Prey Equations . Let x ≥ 0 and y ≥ 0 denote the populations (or their densities) of the prey and the predator. We make the following assumptions about the prey, predator, and their interaction. 1. In the absence of the predator, the prey grows exponentially, i.e., dx/dt = ax for a constant a > 0 when y = 0. 2. In the absence of the prey, the predator dies out exponentially, i.e., dy/dt =- cy for a constant c > 0 when x = 0. 3. The number of encounters between the predator and prey is proportional to the product of their populations. Each encounter tends to promote the growth of the predator, and diminish the prey. The predator grows according to γxy , for a constant γ > 0, and the prey decreases according to- αxy , for a constant α > 0. With this assumptions we obtain the Lotka-Volterra equations that model the predator- prey situation: dx/dt = ax- αxy = x ( a- αy ) , dy/dt =...
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This note was uploaded on 11/29/2011 for the course MATH 334 taught by Professor Dallon during the Fall '08 term at BYU.

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M334Lec39 - Math 334 Lecture#39 9.5 Predator-Prey...

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