In the LotkaVolterra equations, the interaction between the two species is modeled

Chapter 9, Problem 13

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In the LotkaVolterra equations, the interaction between the two species is modeled byterms proportional to the product xy of the respective populations. If the prey population ismuch larger than the predator population, this may overstate the interaction; for example,a predator may hunt only when it is hungry and ignore the prey at other times. In thisproblem we consider an alternative model proposed by Rosenzweig and MacArthur.9(a) Consider the systemx = x1 0.2x 2yx + 6, y = y0.25 + xx + 6.Find all of the critical points of this system.(b) Determine the type and stability characteristics of each critical point.(c) Draw a direction field and phase portrait for this system.

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