I am studying the linear stability of continuous system as a function of two parameters (a and b) and I observe that a hopf bifurcation with frequency w happens along the line described by f(a,b). Now, it turns out that there is a critical point (a_c, b_c), for which w=infinity along the line f(a,b). As the points approach (a_c, b_c) from one side the frequency diverges. I suspect a bifurcation at (a_c, b_c), but I can not identify the right name to look it up. From what I know, this looks like some route to chaos but I don't see how it can lead to a continuously increasing frequency w along f(a,b). Any ideas on how to characterize and understand this transition are welcome.
Thanks in advance,
M