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

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

Using the S1$$ {S}^1 $$‐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 t...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 47; no. 2; pp. 1065 - 1094
Main Authors: Efendiyev, Messoud, Hu, Qingwen
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 30-01-2024
Subjects:
Bifurcation theory
Carbon dioxide
Carbon dioxide concentration
Differential equations
global Hopf bifurcation
Hopf bifurcation
Mathematical models
multiple threshold‐type state‐dependent delays
Oscillations
Respiratory system
S1$$ {S}^1 $$‐equivariant degree
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Summary:Using the S1$$ {S}^1 $$‐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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9700