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Efendiyev, M.A. ; Hu, Q.*

Global Hopf bifurcation for differential equations with multiple threshold-type state-dependent delays.

Math. Meth. Appl. Sci. 47, 1065-1094 (2024)
DOI
Open Access Green as soon as Postprint is submitted to ZB.
Using the (Formula presented.) -equivariant degree, we develop a global Hopf bifurcation theory for system of differential equations with multiple threshold-type state-dependent delays whose prototype is the human respiratory system with multiple blood transport time delays. To establish a theoretic framework for modeling practices of periodic breathing, we further investigate the periodic oscillations of carbon dioxide concentrations in the lung, brain, and tissue compartments and conduct a local and global Hopf bifurcation analysis for the model when varying the commensurate scale of the multiple delays in a transformed system. Such a global Hopf bifurcation will indicate the onset and persistence of the periodic oscillations.
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Publication type Article: Journal article
Document type Review
Corresponding Author
Keywords Global Hopf Bifurcation ; Multiple Threshold-type State-dependent Delays ; Respiratory System ; S1 {s}^1 -equivariant Degree; Control-system; Responses; Instability; Stability
ISSN (print) / ISBN 0170-4214
e-ISSN 1099-1476
Journal Mathematical Methods in the Applied Sciences
Quellenangaben Volume: 47, Issue: 2, Pages: 1065-1094 Article Number: , Supplement: ,
Publisher Wiley
Publishing Place 111 River St, Hoboken 07030-5774, Nj Usa
Non-patent literature Publications
Reviewing status Peer reviewed
Institute(s) Institute of Computational Biology (ICB)
Grants The authors declare no potential conflict of interest.