Suppose x is a predator and y and z are both prey. z grows logistically in...

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Suppose x is a predator and y and z are both prey. z grows logistically in the absence of the predator, while y grows at an exponential rate in the absence of the predator. x dies in the absence of prey. Under these conditions, the predator-prey equations are dx dt dy dt dz dt " = axz+ bxy - cx, = dy 1- gxy, (1 – ²) – jxz, = hz (1- where a, b, c, d, g, h, j, and K are positive constants. (a) The equilibria of (x, y, z) are (0, 0, 0), (0, 0, K), 'd adjK+gh(cak) G bgh (9) (10) (11) (h(ak = c), 0,), (d, 6,0), and K(1-3/h)). Provide a brief biological interpretation of each equilibrium¹. (b) Construct the Jacobian and characteristic polynomial in terms of x, y, and z. Then, for each equilibrium, apply the Routh-Hurwitz conditions to identify under what conditions solutions might converge to each equilibrium. Activate Windows Go to Settings to activate Windows. Suppose x is a predator and y and z are both prey. z grows logistically in the absence of the predator, while y grows at an exponential rate in the absence of the predator. x dies in the absence of prey. Under these conditions, the predator-prey equations are dx dt dy dt dz dt " = axz+ bxy - cx, = dy 1- gxy, (1 – ²) – jxz, = hz (1- where a, b, c, d, g, h, j, and K are positive constants. (a) The equilibria of (x, y, z) are (0, 0, 0), (0, 0, K), 'd adjK+gh(cak) G bgh (9) (10) (11) (h(ak = c), 0,), (d, 6,0), and K(1-3/h)). Provide a brief biological interpretation of each equilibrium¹. (b) Construct the Jacobian and characteristic polynomial in terms of x, y, and z. Then, for each equilibrium, apply the Routh-Hurwitz conditions to identify under what conditions solutions might converge to each equilibrium. Activate Windows Go to Settings to activate Windows.

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Predatorprey Model Analysis a Equilibria and Biological Interpretations The model defines four possible equilibria 0 0 0 This represents the extinction of all populations predator and both prey specie... View the full answer