Mathematical models of bipolar disorder

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

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

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
Volume14
Issue number7
DOIs
StatePublished - Jul 2009

Fingerprint

Disorder
Mathematical Model
Mathematical models
Model
Nonlinear Oscillator
Harmonic Oscillator
Damped
Limit Cycle
Series
Framework

Keywords

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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

Daugherty, D., Roque-Urrea, T., Urrea-Roque, J., Troyer, J., Wirkus, S., & Porter, M. A. (2009). Mathematical models of bipolar disorder. Communications in Nonlinear Science and Numerical Simulation, 14(7), 2897-2908. https://doi.org/10.1016/j.cnsns.2008.10.027

Mathematical models of bipolar disorder. / Daugherty, Darryl; Roque-Urrea, Tairi; Urrea-Roque, John; Troyer, Jessica; Wirkus, Stephen; Porter, Mason A.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 7, 07.2009, p. 2897-2908.

Research output: Contribution to journalArticle

Daugherty, D, Roque-Urrea, T, Urrea-Roque, J, Troyer, J, Wirkus, S & Porter, MA 2009, 'Mathematical models of bipolar disorder', Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 7, pp. 2897-2908. https://doi.org/10.1016/j.cnsns.2008.10.027
Daugherty, Darryl ; Roque-Urrea, Tairi ; Urrea-Roque, John ; Troyer, Jessica ; Wirkus, Stephen ; Porter, Mason A. / Mathematical models of bipolar disorder. In: Communications in Nonlinear Science and Numerical Simulation. 2009 ; Vol. 14, No. 7. pp. 2897-2908.
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