COMPARISON BETWEEN LYAPUNOV AND CLASSICAL METHOD



 
 
 
        Let's consider the second order system:

(1)




    EQUILIBRIUM POINTS
 
 

        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 
 

    EQUILIBRIUM POINTS STABILITY
 

        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.
 
 

    NUMERICAL RESULTS