Bipolar disorder, also known as manic-depression, is a disorder in which a person has mood swings out of proportion or totally unrelated to events in their lives. Bipolar disorder affects as many as 1 percent of the adults in the United States. We focus in particular on bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes. We model a person affected with bipolar II disorder using a Van der Pol oscillator, which is an example of a Lienard oscillator. We then generalize the Van der Pol oscillator to represent the patient after they receive medication. In this paper we analyze the size and stability of limit cycles and support this analysis with numerical simulations.

Granular media is an interesting system to study in pattern formation because no equations are known to describe it. A simple framework called continuum coupled maps is able to reproduce experiments in the area. This will be presented along side a generalization of the model to handle multiple-frequency forcing.