DearMHFmembers,

I have the following problem.

Problem.Find all the singular points of the system

Investigate the stability and determine the type of each singular point.

I know that the critical points of the system are , , and . My problem is determining the stability properties of these points. Please let me know if my idea below is correct. For instance for the point critical point , I linearize the equation at and get

This is possible since the remainders tend to zero, i.e.,

and

.

Since the linearized equations eigenvalues are of opposite sign, we see that the critical point is a saddle point and is therefore unstable. I will repeat the same steps above for each critical point.

Thanks a lot.

bkarpuz