Consider the systemx= xa 0.2x 2yx + 6, y= y0.25 + xx +

Chapter 9, Problem 19

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Consider the systemx= xa 0.2x 2yx + 6, y= y0.25 + xx + 6,where a is a positive parameter. Observe that this system includes the one in above and also the one in in Section 9.5.(a) Find all of the critical points.(b) Consider the critical point in the interior of the first quadrant. Find the eigenvalues ofthe approximate linear system. Determine the value a0 where this critical point changesfrom asymptotically stable to unstable.(c) Draw a phase portrait for a value of a slightly greater than a0. Observe that a limitcycle has appeared. How does the limit cycle change as a increases further?

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