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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 xy , for a constant > 0, and the prey decreases according to- xy , for a constant > 0. With this assumptions we obtain the Lotka-Volterra equations that model the predator- prey situation: dx/dt = ax- xy = x ( a- y ) , dy/dt =...
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