Abstract
We extend the Grodins model of human cardiovascular‐respiratory system with multiple blood transport time delays into a model with four threshold type state‐dependent delays, in order to investigate the asymptotic stability of carbon dioxide concentrations in the lung, brain, cerebrospinal fluid, and tissue compartments. We show that the extended model can be transformed into a model with four discrete time delays and obtain sufficient conditions for local and global asymptotic stabilities of the extended model by constructing Lyapunov functionals. Numerical simulations are presented to illustrate the general results.
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