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.,
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