Global exponential stability for the Mackey–Glass model of respiratory dynamics with a control term | Zendy

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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.

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