Consider the predator/prey model x\' = 2x - x2 - xy y\' = -1y + xy. Find the lin

Question

Consider the predator/prey model x' = 2x - x2 - xy y' = -1y + xy. Find the linearization of this system at the second of the critical points you found in problem 5. [x' y'] = A[x y], where A = Then solve this to find the eigenvalues of the linearized system (enter any complex numbers you may obtain by using "i" for . For real answers, enter them in ascending order; for complex, enter the a - ib root before a + ib): lambda1= , lambda2 = The critical point is unstable stable asymptotically stable and is a(n) spiral sink spiral source center improper node node saddle point.

Explanation / Answer

A=(2-x -x)

( 0 x-1)

lambda 1=x-1 ; lambda2= 2-x

critical point is stable

a(n) is node

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