Let's consider the second order system:(1)

For a system described by , the equilibrium points are obtained by solving the equation . For the equation (1):

The resolution of this system leads to three equilibrium points: , , and

Jacobean matrix of the system is

For this matrix becomes

Its eigenvalue is –2, which is negative. So this point is a node and it is asymptotically stable.

For this matrix becomes

Its eigenvalues are 2 and –2, one positive and one negative. So, this point is unstable, it's a saddle point.

For this matrix becomes

Its eigenvalues are 0 and 1. This point is also unstable.