This paper discusses the dynamics and bifurcation theory of equivariant dynamical systemsnear
relative equilibria, that is, group orbits invariant under the flow of an equivariant vector …

The geometric approach to singular perturbation problems is based on powerful methods
from dynamical systems theory. These techniques have been very successful in the case of …

We give a geometric analysis of relaxation oscillations and canard cycles in singularly perturbed
planar vector fields. The transition from small Hopf-type cycles to large relaxation cycles…

One phenomenon in the dynamics of differential equations which does not typically occur in
systems without symmetry is heteroclinic cycles. In symmetric systems, cycles can be robust …

Mixed mode oscillations combine features of small oscillations and large oscillations of
relaxation type. We describe a mechanism for mixed mode oscillations based on the presence of …

Systems possessing symmetries often admit heteroclinic cycles that persist under perturbations
that respect the symmetry. The asymptotic stability of such cycles has previously been …

Mixed-mode dynamics is a complex type of dynamical behavior that is characterized by a
combination of small-amplitude oscillations and large-amplitude excursions. Mixed-mode …

Folded saddle-nodes occur generically in one parameter families of singularly perturbed
systems with two slow variables. We show that these folded singularities are the organizing …

We consider the dynamics of singularly perturbed differential equations near points where
the critical manifold has a transcritical or a pitchfork singularity. Our main tool is the recently …

The rs1061170T/C variant encoding the Y402H change in complement factor H (CFH) has
been identified by genome-wide association studies as being significantly associated with …