Reference no: EM131257358

Consider a prey species (rabbits) with population size x(t) and a predator species (foxes) with population size y(t). Suppose that in the absence of the predator, the prey population would experience exponential growth with rate parameter a. In the absence of prey, the predator dies out (exponential decay with parameter d). Further suppose that the rate of predators catching prey is proportional to x(t)y(t), and this leads to a loss of prey (parameter beta) and an increase in predators (parameter gamma). These asumptions lead to probably the simplest form of a predator-prey system: Find the critical points of the system and describe them in biological terms. Calculate the Jacobian matrix and linearize around each critical point. Classify the critical points and sketch the vector field by hand.