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A note on global attractivity in models of hematopoiesis. (English) Zbl 0933.92013

Ukr. Math. J. 50, No. 1, 3-12 (1998) and Ukr. Mat. Zh. 50, No. 1, 5-12 (1998).
See the review in Zbl 0893.92012.

MSC:

92C30 Physiology (general)
34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology

Citations:

Zbl 0893.92012
Full Text: DOI

References:

[1] Mackey, M. C.; Glass, L., Oscillation and chaos in physiological control systems, Science, 197, 287-289 (1977) · Zbl 1383.92036 · doi:10.1126/science.267326
[2] Gopalsamy, K.; Kulenovich, M. R. S.; Ladas, G., Oscillations and global attractivity in models of hematopoiesis, J. Dynam. Different. Equat., 2, 2, 117-132 (1990) · Zbl 0694.34057 · doi:10.1007/BF01057415
[3] Ivanov, A. F.; Sharkovsky, A. N., Oscillations in singularly perturbed delay equations, Dvnam. Rep., 1, 164-224 (1991) · Zbl 0755.34065
[4] Karakostas, G.; Philos, Ch. G.; Sficas, Y. G., Stable steady state of some population models, J Dynam. Different. Equat., 4, 1, 161-190 (1989) · Zbl 0744.34071 · doi:10.1007/BF01048159
[5] Mallet-Paret, J.; Nussbaum, R. D., Global continuation and asymptotic behaviour for periodic solutions of differential delay equations, Ann. Mat. Pura Appl, 145, 33-128 (1986) · Zbl 0617.34071 · doi:10.1007/BF01790539
[6] Györi, I.; Ladas, G., Oscillations Theory of Delay Differential Equations with Applications (1991), London: Oxford University Press, London · Zbl 0780.34048
[7] Gopalsamy, K., Stability and oscillations in delay differential equations of population dynamics, Math. Appl., 74, 501-501 (1992) · Zbl 0752.34039
[8] Ivanov, A. F., On global stability in nonlinear discrete models, Nonlinear Anal., 23, 11, 1383-1389 (1994) · Zbl 0842.39005 · doi:10.1016/0362-546X(94)90133-3
[9] Karakostas, G.; Philos, Ch. G.; Sficas, Y. G., Stable steady state of some population models, J Dynam. Different. Equat., 17, 11, 161-190 (1992) · Zbl 0744.34071 · doi:10.1007/BF01048159
[10] Wazewska-Czyzewska, M.; Lasota, A., Mathematical problems of the red-blood cell system, Ann. Pol. Math. Soc., Ser. III. Appl. Math., 6, 23-40 (1976) · Zbl 0363.92012
[11] Györi, I.; Trofimchuk, S., Global Attractivity in x’ (t) = -δx(t) + pf(x(t-τ)) (1996), Veszprem: University of Veszprem, Veszprem · Zbl 0965.34064
[12] Hale, J. K., Theory of Functional-Differential Equations (1977), Berlin: Springer, Berlin · Zbl 0352.34001
[13] Singer, D., Stable orbits and bifurcation of maps of the interval, SIAM J. Appl. Math., 35, 2, 260-267 (1978) · Zbl 0391.58014 · doi:10.1137/0135020
[14] Sharkovskii, A. N.; Kolyada, S. F.; Sivak, A. G.; Fedorenko, V. V., Dynamics of One-Dimensional Dynamical Systems (1989), Kiev: Naukova Dumka, Kiev · Zbl 0759.58001
[15] J. K. Hale, “Asymptotic behavior of dissipative systems,” in: Mathematical Surveys and Monographs, No. 25, Am. Math. Soc., Providence (1988). · Zbl 0642.58013
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