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Global exponential stability for the Mackey–Glass model of respiratory dynamics with a control term
Author(s) -
Wentao Wang
Publication year - 2016
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.3519
Subject(s) - mathematics , exponential stability , term (time) , stability (learning theory) , dynamics (music) , lyapunov function , exponential function , control theory (sociology) , control (management) , mathematical analysis , computer science , nonlinear system , physics , quantum mechanics , machine learning , artificial intelligence , acoustics
This paper is concerned with the stability of positive periodic solutions for the Mackey–Glass model of respiratory dynamics with a control term. We prove the existence, positivity, and permanence of solutions, which help to deduce the global exponential stability of positive periodic solutions for this model. Our method relies upon a differential inequality technique and a Lyapunov functional. At the end, we give an example with numerical simulations to demonstrate the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.