Higher-dimensional separation principle for the analysis of relaxation oscillations in nonlinear systems: application to a model of HIV infection

IMA J Math Appl Med Biol. 2000 Sep;17(3):243-61.

Abstract

In this paper, geometric and singular perturbation arguments are utilized to develop a separation condition for the identification of limit cycles in higher-dimensional (n > or = 4) dynamical systems characterized by highly diversified time responses, in which there exists an (n - 3)-dimensional subsystem which quickly reaches a quasi-steady state. The condition, which has been used up to now to analyze relaxation oscillation in slow-fast systems, is extended to accommodate dynamical systems in which more state variables are involved in a special manner which still allows for the use of singular perturbation techniques. Application is then made to a model of human immunodeficiency virus infection in T helper (TH) cell clones with limiting resting TH cell supply.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Clone Cells / virology
  • Computer Simulation
  • HIV / growth & development
  • HIV Infections / etiology*
  • HIV Infections / virology
  • Humans
  • Mathematics
  • Models, Biological*
  • Nonlinear Dynamics
  • Oscillometry
  • T-Lymphocytes, Helper-Inducer / virology