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The Mackey–Glass model of respiratory dynamics: Review and new results
- Source :
- Nonlinear Analysis: Theory, Methods & Applications. 75:6034-6052
- Publication Year :
- 2012
- Publisher :
- Elsevier BV, 2012.
-
Abstract
- a b s t r a c t Since the celebrated Mackey–Glass model of respiratory dynamics was introduced in 1977, many results on its qualitative behavior have been obtained, including oscillation, stability and chaos. The paper reviews some known properties and presents new results for more general models: equations with time-dependent parameters, several delays, a positive periodic equilibrium and distributed delays. The problems considered in the paper involve existence, positivity and permanence of solutions, oscillation and global asymptotic stability. In addition, some general approaches to the study of nonlinear nonautonomous scalar delay equations are outlined. The paper generalizes and unifies existing results and provides an outlook on further studies.
- Subjects :
- Oscillation
Applied Mathematics
010102 general mathematics
Mathematical analysis
Dynamics (mechanics)
Scalar (physics)
010103 numerical & computational mathematics
01 natural sciences
Stability (probability)
Nonlinear system
Exponential stability
Applied mathematics
0101 mathematics
Analysis
Mathematics
Subjects
Details
- ISSN :
- 0362546X
- Volume :
- 75
- Database :
- OpenAIRE
- Journal :
- Nonlinear Analysis: Theory, Methods & Applications
- Accession number :
- edsair.doi...........f692617739955c2023e48f6c43c74cf0