Stability analysis

After linearization of the system (6)-(7) in the vicinity of the equilibrium points, we get the Jacobi matrix:

Let us consider the point . Then

and the corresponding eigenvalues are equal to:

i.e. this equilibrium is a stable node, if
 
and it is an unstable saddle, if
 
Since for any , then , and any equilibrium is stable.

If then

and the corresponding eigenvalues are equal to

Since for any , then , and the equilibrium with cannot be an unstable node.

This equilibrium is a saddle point if

If , we have a stable node or stable focus, moreover for the latest