  We use limit cycle oscillators to model Bipolar II disorder, which is
characterized by alternating hypomanic and depressive episodes and afflicts
about one percent of the United States adult population. We consider two
nonlinear oscillator models of a single bipolar patient. In both frameworks, we
begin with an untreated individual and examine the mathematical effects and
resulting biological consequences of treatment. We also briefly consider the
dynamics of interacting bipolar II individuals using weakly-coupled,
weakly-damped harmonic oscillators. We discuss how the proposed models can be
used as a framework for refined models that incorporate additional biological
data. We conclude with a discussion of possible generalizations of our work, as
there are several biologically-motivated extensions that can be readily
incorporated into the series of models presented here.
