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Problem 6. Our ecologist from problem 4 is also studying the predation of predators y on one of the herbivores r. She uses the following

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Problem 6. Our ecologist from problem 4 is also studying the predation of predators y on one of the herbivores r. She uses the following system of equations to model the populations where the parameter a measures the magnitude of the predation. I = 1(3 - ay) y = y(x - 1.5). a.) Find the critical point at which both populations are positive, in terms of a. b. ) Show that the eigenvalue is independent of the parameter a. c.) For the value a = 1, find the general solution to the linearized equa- tions at the point found in part a

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