Higher-dimensional separation principle for the analysis of relaxation oscillations in nonlinear systems: application to a model of HIV infection.
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.
Lenbury
Y
Y
Department of Mathematics, Mahidal University, Bangkok, Thailand.
Ouncharoen
R
R
Tumrasvin
N
N
D002999:Clone Cells / Q000821:virology; D003198:Computer Simulation; D006678:HIV / Q000254:growth & development; D015658:HIV Infections / Q000209:etiology* / Q000821:virology; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D017711:Nonlinear Dynamics; D009991:Oscillometry; D006377:T-Lymphocytes, Helper-Inducer / Q000821:virology