Example A

Consider the system

Suppose we have found the equilibrium (**,_>■*) = (2,1) (it is easily verified that r(2,1) = s(2,l) = 0). Is the equilibrium stable or unstable? By partial differentiation and insertion of (2,1) we get:

r[ (x, y) = -2x,r'(x, y) = 1, s', (x, y) = 1, < (x, y) = -2y

We conclude that (2,1) is a locally stable equilibrium for the system (A.117).

EXERCISE A.17

Consider the system a = r'x(x*,y*), c^r'(x*,y*), b=s'x(x*,y*), d = s[ (x*,y*)-

=> a = - 4, 6 = 1, c = l, d=- 2 => a + d=- 6<0, ad + bc=l>Q.

Find all equilibria of the system. Are they stable or unstable?

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