Amy Veprauskas
My research interests are in mathematical models of population and evolutionary dynamics.
My current research focus is in stage-structured population models with imprimitive projection matrices. In models containing
imprimitive projection matrices, the extinction equilibrium destabilizes due to multiple eigenvalues leaving the region of stability.
This results in multiple possible steady states, including oscillations in which certain stages are temporally separated. Imprimitive matrices commonly appear in models of semelparous species, which are characterized by one reproductive event often
followed by death. Biologically these types of cycles have been observed in the well known periodical outbreaks of cicadas
and other periodical insects. In my research, I have applied local bifurcation analysis to both discrete and continuous-time
structured models to study the nature and stability of these high co-dimension bifurcations.