Dear MHF members,
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.,
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.