Global stability for a class of delay differential equations

Applied Mathematics Letters

Volumn 17, Issue 6, 2004, Pages 581-584

  Forys U ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Delay differential equation; Ehrlich ascites tumour; Global stability; Hopf bifurcation; Logistic equation; Stability

Indexed keywords

BIFURCATION (MATHEMATICS); FUNCTION EVALUATION; MATHEMATICAL MODELS; MEDICINE; PARAMETER ESTIMATION; SET THEORY; TUMORS;

DELAY DIFFERENTIAL EQUATIONS; EHRLICH ASCITES TUMOR; GLOBAL STABILITY; HOPF BIFURCATION; LOGISTIC EQUATION;

DIFFERENTIAL EQUATIONS;

EID: 3242720484     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2003.01.012     Document Type: Article

References (11)

1. G.E. Hutchinson, Circular casual systems in ecology, Ann. N.Y. Acad. Sci. 50, 221-246, (1948).
2. R. Schuster and H. Schuster, Reconstruction models for the Ehrlich ascites tumor of the mouse, In Mathematical Population Dynamics, Volume 2, (Edited by O. Arino, D. Axelrod and M. Kimmel), Wuertz, Winnipeg, (1995).
3. U. Foryś and M. Kolev, Time delays in proliferation and apoptosis for solid avascular tumour, Warsaw University, RW 02-10 (110), (Preprint, August 2002); Mathematical Modelling of Population Dynamics, Volume 63, Banach Center Publications, Warsaw, (2004).
4. U. Foryś and M. Kolev, Time delays in proliferation and apoptosis for solid avascular tumour, Warsaw University, RW 02-10 (110), (Preprint, August 2002); Mathematical Modelling of Population Dynamics, Volume 63, Banach Center Publications, Warsaw, (2004).
5. M. Kirkilionis, O. Diekman, B. Lisser, M. Nool, B. Sommeijer and A. deRoos, Numerical continuation of equilibria of physiologically structured population models, I. Theory, Math. Models Methods Appl. Sci. 6, 1101-1127, (2001).
6. J. Hale, Theory of Functional Differential Equations, Springer, New York, (1987).
7. U. Foryś and A. Marciniak-Czochra, Delay logistic equation with diffusion, In Proceedings of VIII National Conference on Mathematics Applied to Biology and Medicine, Lajs 2002, (Edited by U. Foryś and M. Ziółko), Warsaw, (2002).
8. U. Foryś and A. Marciniak-Czochra, Logistic equation in tumour growth modelling, Int. J. Appl. Math. Comp. Sci. 13 (3), 317-325, (2003).
9. M. Bodnar, The nonnegativity of solutions of delay differential equations, Appl. Math. Lett. 13 (6), 91-95, (2000).
10. U. Foryś, On the Mikhailov criterion and stability of delay differential equations, Warsaw University, RW 01-14 (97), (Preprint, November 2001).
11. U. Foryś Biological delay systems and the Mikhailov criterion of stability, J. Biol. Sys. 13 (1), 1-16, (2004).