I have studied bifurcation theory on the context of population models (both continuous and discrete). However, these have been models with just one parameter.
I would like to know where to look for generalisations of this theory for more than one parameter, and how it works for partial differential equations.
As all I have seen has been in the context of population, I am curious to know other applications of this theory in other areas (especially geometry and topology).
Which areas would you advice to study before?
Which books or articles would you recommend to start exploring these questions?
Start with Kuznetsov's Elements of applied bifurcation theory and follow the references there that are more interesting for you.