Mathematical models of panic disorder

Takao Fukano, Yukio Gunji

Research output: Contribution to journalArticle

Abstract

The dynamics of panic attacks in both functional individuals and panic disorder patients are qualitatively evaluated by using coupled nonlinear differential equations. Each panic attack is described by two variables, fear and physical symptoms. Different thresholds for these variables are defined for functional individuals, patients in the acute phase, and patients in the chronic phase. Integral lines, vector fields, and time series of solutions, based on the proposed coupled nonlinear differential equations, are shown. The efficacy of treatment and severity of each panic attack are also evaluated. Under our hypothesized condition, it is shown that particular pharmacological treatment could change the final states of patients in the acute phase, but could not change either the final states of patients in the chronic phase or those of functional individuals. Our model is consistent with the well-known major features of panic attacks, and sheds new light on the dynamics of panic attacks.

Original languageEnglish
Pages (from-to)457-470
Number of pages14
JournalNonlinear Dynamics, Psychology, and Life Sciences
Volume16
Issue number4
Publication statusPublished - 2012 Oct
Externally publishedYes

Fingerprint

Disorder
Differential equations
Attack
Mathematical Model
Mathematical models
Time series
Acute
Nonlinear Differential Equations
Curvilinear integral
Efficacy
Vector Field
Model

Keywords

  • Differential equations
  • Mathematical modeling
  • Medication
  • Nonlinear dynamical systems
  • Panic disorder

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Mathematical models of panic disorder. / Fukano, Takao; Gunji, Yukio.

In: Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 16, No. 4, 10.2012, p. 457-470.

Research output: Contribution to journalArticle

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