Mathematical models of bipolar disorder

Darryl Daugherty, Tairi Roque-Urrea, John Urrea-Roque, Jessica Troyer, Stephen Wirkus, Mason A. Porter

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear 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.

Original languageEnglish (US)
Pages (from-to)2897-2908
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Issue number7
StatePublished - Jul 2009


  • Averaging
  • Bipolar disorder
  • Lienard oscillators
  • Limit cycle oscillators

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics


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