Connections between compartmental systems with pipes and integro-differential equations

Mathematical Modelling - Tập 7 Số 9-12 - Trang 1215-1238 - 1986
István Győri1
1Computing Centre Szeged University, School of Medicine Szeged, Hungary

Tóm tắt

Từ khóa


Tài liệu tham khảo

Araki, 1979, On stability criteria for the composite systems including time delays, Trans. SICE, 15, 267, 10.9746/sicetr1965.15.267

Arino, 1979, Comportement des solutions de x'(t) + f(t, x(t) = f(t − 1, x(t − 1)), C.R.A.S., 28, 937

Atkins, 1969

Bellman, 1971, Topics in pharmacokinetics II: Identification of time-lag processes, Math. Biosci., 11, 337, 10.1016/0025-5564(71)90092-7

Brown, 1980, Compartmental system analysis: State of the art, IEEE Trans. Biomed. Eng., BME-27, 1, 10.1109/TBME.1980.326685

Brown, 1979, Some observations on the physical realizability of compartmental models with delays, IEEE Trans. Biomed. Eng., BME-26, 646, 10.1109/TBME.1979.326549

Cooke, 1976, A periodicity threshold theorem for epidemics and population growth, Math. Biosci., 31, 87, 10.1016/0025-5564(76)90042-0

Coppel, 1965

Driver, 1977

Györi, 1982, Delay differential and integro-differential equations in biological compartmental models, Systems Sci. (Wroclaw), 8, 167

Györi, 1981, Compartmental systems with pipes, Math. Biosci., 53, 223, 10.1016/0025-5564(81)90019-5

Haddock, 1981, Liapunov-Razumikhin functions and invariance principle for functional differential equations

Jacquez, 1972, Compartmental Analysis in Biology and Medicine

Jacquez, 1979, Compartmental models of biological systems: Linear and nonlinear, Applied Nonlinear Analysis, 185, 10.1016/B978-0-12-434180-7.50021-8

Kanyar, 1981, Parameter estimation of the radiocardiogram using compartmental models with pipes, Vol. 34, 229

Lakshmikantham, 1969, Differential and Integral Inequalities (II)

Lewis, 1980, Insensitivity of a class of nonlinear compartmental systems to the introduction of arbitrary time delays, IEEE Trans. Circ. Syst., CAS-27, 604, 10.1109/TCS.1980.1084867

Maeda, 1979, Some results on nonlinear compartmental systems, IEEE Trans. Circ. Syst., CAS-26, 203, 10.1109/TCS.1979.1084618

Maeda, 1978, Asymptotic behavior of nonlinear compartmental systems: Nonoscillation and stability, IEEE Trans. Circ. Syst., CAS-25, 372, 10.1109/TCS.1978.1084490

Mazanov, 1976, Stability of multi-pool models with lags, J. Theoret. Biol., 59, 429, 10.1016/0022-5193(76)90181-8

Nagy, 1965

Ohta, 1981, Qualitative analysis of nonlinear quasi-monotone dynamical systems described by functional-differential equations, IEEE Trans. Circ. Syst., CAS-28, 138, 10.1109/TCS.1981.1084959

Reeve, 1962, Mathematical models describing the distribution of 131I-albumin in man, J. Lab. Clin. Med., 60, 923

Rubinov, 1975

Sandberg, 1978, On the mathematical fundations of compartmental analysis in biology, medicine and ecology, IEEE Trans. Circ. Syst., CAS-25, 273, 10.1109/TCS.1978.1084473

Sheppard, 1948, The theory of study of transfers within a multi-compartment system using isotopic tracers, J. Appl. Phys., 19, 70, 10.1063/1.1697874

Tokumaru, 1975, Macroscopic stability of interconnected systems, IFAC sixth conf.

Wagner, 1979

Wendel, 1961, The application of hydrodynamics to elucidate the interrelationships of various body compartment volumes, Phys. Med. Biol., 5, 411, 10.1088/0031-9155/5/4/303