IMA Journal of Mathemathics Applied in Medicine and Biology. Vol.17, No.3 (2000), 243-261
Suggested Citation
Youngwimon Lenbury, Bujira Ouncharoen, Nardtida Tumrasvin Higher-dimensional separation principle for the analysis of relaxation oscillations in nonlinear systems: Application to a model of HIV infection. IMA Journal of Mathemathics Applied in Medicine and Biology. Vol.17, No.3 (2000), 243-261. Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/25813
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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 ≥ 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.
