Mathematical study of periodic breathing as an instability of the respiratory system

DOI10.1016/0025-5564(93)90076-MzbMath0782.92006WikidataQ52398238 ScholiaQ52398238MaRDI QIDQ2365588

Bruno Vielle, Gilbert A. Chauvet

Publication date: 29 June 1993

Published in: Mathematical Biosciences (Search for Journal in Brave)

zbMATH Keywords

time delayperiodic breathinglaw of mass conservationexplicit analytical index of stabilityfeedback control loopperipheral controller systemrespiratory stabilitytwo-dimensional dynamical model

Mathematics Subject Classification ID

Stability theory of functional-differential equations (34K20) Physiology (general) (92C30)

Related Items (7)

Stability and bifurcation of a human respiratory system model with time delay ⋮ Oxygen therapy for management of periodic breathing : a theoretical approach ⋮ Models of Cheyne-Stokes respiration with cardiovascular pathologies ⋮ Hopf bifurcation analysis in a delayed human respiratory system ⋮ Modeling instability in the control system for human respiration: Applications to infant non-REM sleep ⋮ Delay equation analysis of human respiratory stability ⋮ A model of the effects of fluid variation due to body position on Cheyne-Stokes respiration

Cites Work

• Stability of functional differential equations
• Ordinary and delay differential equations
• Necessary and sufficient conditions for delay-independent stability of linear autonomous systems
• Roots of the Transcendental Equation Associated with a Certain Difference-Differential Equation
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