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

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 ≥ 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 (T _H ) cell clones with limiting resting T _H cell supply.

oscillations, higher-dimensional nonlinear systems, separation principle, HIV model