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Asymptotic stability of the human respiratory system with multiple state‐dependent delays
Author(s) -
Hu Qingwen
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5811
Subject(s) - mathematics , exponential stability , stability (learning theory) , lyapunov function , cerebrospinal fluid , respiratory system , state (computer science) , control theory (sociology) , computer science , nonlinear system , physics , medicine , neuroscience , biology , algorithm , control (management) , quantum mechanics , machine learning , artificial intelligence
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.