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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)

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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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