#### Poster Title

P-50 Proving the existence of 2-cycle bifurcations in a discrete-time model of seabird reproduction

#### Abstract

In mathematical biology, discrete-time dynamical systems can be used to model the progression of seabirds through various stages of their reproductive cycles. Burton and Henson posed a simple mathematical model of seabird reproduction; they showed the existence and uniqueness of a branch of stable equilibria that undergoes a 2-cycle bifurcation as colony density increases. Here we prove for a modified, more realistic model that a similar equilibrium branch exists with an analogous 2-cycle bifurcation appearing as the parameter representing colony density increases.

#### Location

Buller Hallway

#### Start Date

3-7-2014 2:30 PM

#### End Date

3-7-2014 4:00 PM

P-50 Proving the existence of 2-cycle bifurcations in a discrete-time model of seabird reproduction

Buller Hallway

In mathematical biology, discrete-time dynamical systems can be used to model the progression of seabirds through various stages of their reproductive cycles. Burton and Henson posed a simple mathematical model of seabird reproduction; they showed the existence and uniqueness of a branch of stable equilibria that undergoes a 2-cycle bifurcation as colony density increases. Here we prove for a modified, more realistic model that a similar equilibrium branch exists with an analogous 2-cycle bifurcation appearing as the parameter representing colony density increases.

## Acknowledgments

Research supported by the National Science Foundation

Advisor: Shandelle Henson, Mathematics