Bifurcation theory is the study of qualitative changes of the dynamics as a parameter of the system varies. We will focus on local bifurcations for vector fields. A typical situation is when the vector field admits an equilibrium where nonzero eigenvalues of the linearization cross the imaginary axis as the parameter varies. This leads to Hopf bifurcation: the appearance of periodic oscillations around the equiibrium. Other invariant sets and heteroclinic connections, however, might also arise nearby. We will explore the bifurcation zoo and illustrate the theory by examples coming from physics, biology and other fields of applications.
See also the lecture "Dynamical Systems 3 - Paralipomena".
Prerequisites are Dynamical Systems 1 and/or 2.