Stability of equillibrium points

Question

Is an equilibrium point stabile if a relevant eigenvalue equal to 1?

Answer 1

From the theorem of fixed points. we have

1) a stable fixed point iff Re[λ_i] < 0 , for all eigenvalues of the matrix and

2) an unstable fixed point if Re[λ_i] > 0, for some eigenvalues of the matrix

Your eigenvalue is λ= 1 >0, therefore the point is an unstable fixed point.