Suppose that the system ̇x=X(x)has a finite number of equilibrium points, each of which is either anode, a centre, a spiral, or a saddle point, of the elementary types discussed in Section 2.5, and...

Suppose that the system ̇x=X(x)has a finite number of equilibrium points, each of which is either anode, a centre, a spiral, or a saddle point, of the elementary types discussed in Section 2.5, and assumeth at
 Show that the total number of nodes, centres, and spirals is equal to the total number ofsaddle points plus two.