Parameter Dependent Stability/Instability in a Human Respiratory Control System Model

In this paper a computational procedure is presented to study the development of stable/unstable patterns in a system of three nonlinear, parameter dependent delay differential equations with two transport delays representing a simplified model of human respiration. It is demonstrated using simulations how sequences of changes in internal and external parameter values can lead to complex dynamic behavior due to forced transitions between stable/unstable equilibrium positions determined by particular parameter combinations. Since changes in the transport delays only influence the stability/instability of an equilibrium position a stability chart is constructed in that case by finding the roots of the characteristic equation of the corresponding linear variational system. Illustrative examples are included.