Stability analysis of Human Respiratory System

Chemical Regulation of Human Respiratory System is a complex dynamical system. Primary function of this system is to regulate gas concentrations in the Blood. It is modeled by Nonlinear Delay Differential Equations. Several dynamical models for respiratory regulation are available in the literature, which are broadly classified as Comprehensive and Minimal Models. Minimal models are derived from the comprehensive models with some assumptions and are linearized for simplified analysis. Current literatures in these mathematical modeling approaches are directed towards describing pathological conditions, giving little thrust for the prediction. Analyses of these systems are not straightforward because of the variable time delay. From the system's point of view, increasing delay makes the system oscillatory. Physiologically, delay depends on the blood flow. In this model, delay in feedback loop of alveolar oxygen and carbon dioxide partial pressures make the system oscillatory, causing discomfort or fatal to the subject. Present analysis is motivated to find out the range of delay for comfortable operation of the system.