Stability of the human respiratory control system: I. Analysis of a two-dimensional delay state-space model

Journal of Mathematical Biology

Volumn 41, Issue 1, 2000, Pages 45-79

  Batzel, J J ^a   Tran, H T ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Delay dependent stability; Instability; Numerical simulations; Respiratory control models; Time delay

Indexed keywords

CARBON DIOXIDE; OXYGEN;

ADULT; ARTICLE; BIOLOGICAL MODEL; BRAIN; COMPUTER SIMULATION; CONGESTIVE HEART FAILURE; FEEDBACK SYSTEM; HUMAN; PATHOPHYSIOLOGY; PHYSIOLOGY; RESPIRATORY FUNCTION; STATISTICAL MODEL;

ADULT; BRAIN; CARBON DIOXIDE; COMPUTER SIMULATION; FEEDBACK; HEART FAILURE, CONGESTIVE; HUMANS; LINEAR MODELS; MODELS, BIOLOGICAL; OXYGEN; RESPIRATORY PHYSIOLOGY;

EID: 0034223127     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850000044     Document Type: Article

References (20)

1. Batzel, J.J., Tran, H.T.: Modeling variable delay and instability in the control system for human respiration: Applications to infant non-rem sleep. J. of Applied Math. and Computation, 110, 1-51 (2000)
2. Boese, F.G.: Comments on "On the zeros of some transcendental equations" by K.L. Cooke and P. van den Driessche, preprint
3. Carley, D.W., Shannon, D.C.: A minimal mathematical model of human periodic breathing. J. Appl. Physiol., 65 (3), 1400-1409 (1988)
4. Cleave, J.P., Levine, M.R., Fleming, P.J., Long, A.M.: Hopf bifurcations and the stability of the respiratory control system. J. Theor. Biol., 119, 299-318 (1986)
5. Cooke, K., Turi, J.: Stability, instability in delay equations modeling human respiration. J. Math. Biol., 32, 535-543 (1994)
6. Cooke, K., van den Driessche, P.: On zeroes of some transcendental equations. Funkcialaj Ekvacioj 29, 77-90 (1986)
7. Cunningham, D.C., Robbins, P.A., Wolff, C.B.: Integration of respiratory responses. Handbook of Physiology. The Respiratory System, Part II Fishman A.P. ed. American Physiol. Soc., Bethesda Md., 475-528 (1986)
8. Dieudonne, J.: Foundations of Modern Analysis. Academic Press, N.Y. (1960)
9. 2 control of the respiratory system: plant dynamics and stability analysis. Annals of Biomed. Eng., 16, 445-461 (1988)
10. El'sgol'ts, L.E., Norkin, S.B.: Introduction to the Theory and Applications of Differential Equations with Deviating Arguments. Academic Press, N.Y. (1973)
11. Glass, L., Mackey, M.C.: Pathological conditions resulting from instabilities in physiological control systems. Annal. N.Y. Acad. Sci., 316, 214-235 (1979)
12. Grodins, F.S., Buell, J., Bart, A.J.: Mathematical analysis and digital simulation of the respiratory control system. J. Appl. Physiology, 22 2, 260-276 (1967)
13. Guyton, A.C.: Physiology of the Human Body. Saunders, Philadelphia (1984)
14. Hale, J.K., Verduyn Lunel, S.M.: Introduction to Functional Differential Equations. Springer-Verlag, N.Y. (1993)
15. Khoo, M.C.K: Periodic breathing. The Lung: scientific foundations. Crystal R. G. and West J.B. et al. Raven Press Ltd., New York, 1419-1431 (1991)
16. Khoo, M.C.K., Gottschalk, A., Pack, A.I.: Sleep-induced periodic breathing and apnea: A theoretical Study. J. Applied Physiol., 70 5, 2014-2024 (1991)
17. Khoo, M.C.K, Kronauer, R.E., Strahl, K.P., Slutsky, A.S.: Factors inducing periodic breathing in humans: a general model. J. Appl. Physiol., 53 3, 644-659 (1982)
18. Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics (1993) Mathematics in Science and Engineering 191-Academic Press, Boston Mass.
19. Mackey, M.C., Glass, L.: Oscillations and chaos in physiological control systems. Science 197, 287-289 (1977)
20. West, J.B.: Respiratory Physiology. Williams and Willaims Co. (1979)