Global attractivity in scalar delayed differential equations with applications to population models

Journal of Mathematical Analysis and Applications

Volumn 289, Issue 1, 2004, Pages 35-54

  Faria, Teresa ^a  

^a UNIVERSITY OF LISBON   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0347577837     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.08.013     Document Type: Article

References (23)

1. K. Gopalsamy, Stability and Oscillation in Delay Differential Equations of Population Dynamics, Kluwer Academic, Dordrecht, 1992.
2. K. Gopalsamy, M.R.S. Kulenović, G. Ladas, Environmental periodicity and time delays in a "food-limited" population model, J. Math. Anal. Appl. 147 (1990) 545-555.
3. E.A. Grove, G. Ladas, C. Qian, Global attractivity in a "food-limited" population model, Dynamic Systems Appl. 2 (1993) 243-249.
4. I. Györi, A new approach to the global stability problem in a delay Lotka-Volterra differential equation, Math. Comput. Modelling 31 (2000) 9-28.
5. J.R. Haddock, Y. Kuang, Asymptotic theory for a class of nonautonomous delay differential equations, J. Math. Anal. Appl. 168 (1992) 147-162.
6. T. Krisztin, On stability properties for one-dimensional functional differential equations, Funkcial. Ekvac. 34 (1991) 241-256.
7. Y. Kuang, Global stability for a class of nonlinear nonautonomous delay equations, Nonlinear Anal. 17 (1991) 627-634.
8. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, London, 1993.
9. E. Liz, M. Pinto, G. Robledo, V. Tkachenko, S. Trofimchuk, Wright type delay differential equations with negative Schwarzian, Disc. Cont. Dyn. Systems 9 (2003) 309-321.
10. H. Matsunaga, R. Miyazaki, T. Hara, Global attractivity results for nonlinear delay differential equations, J. Math. Anal. Appl. 234 (1999) 77-90.
11. Y. Muroya, On Yoneyama's 3/2 stability theorems for one-dimensional delay differential equations, J. Math. Anal. Appl. 247 (2000) 314-322.
12. C. Qian, Global Attractivity in nonlinear delay differential equations, J. Math. Anal. Appl. 197 (1996) 529-547.
13. J.W.-H. So, J.S. Yu, Global attractivity for a population model with time delay, Proc. Amer. Math. Soc. 123 (1995) 2687-2694.
14. J.W.-H. So, J.S. Yu, On the uniform stability for a "food-limited" population model with time delay, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995) 991-1002.
15. J.W.-H. So, J.S. Yu, Global stability for a general population model with time delays, in: S. Ruan, G. Wolkowicz, J. Wu (Eds.), Differential Equations with Applications to Biology, in: Fields Inst. Commun., Vol. 21, 1999, pp. 447-457.
16. J.W.-H. So, J.S. Yu, M.-P. Chen, Asymptotic stability for scalar delay differential equations, Funkcial. Ekvac. 39 (1996) 1-17.
17. J. Surgie, On the stability for a population growth equation with time delay, Proc. Roy. Soc. Edinburgh Sect. A 120 (1992) 179-184.
18. X. Tang, X. Zou, A 3/2 stability result for a regulated logistic growth model, Disc. Cont. Dyn. Systems 2B (2002) 265-278.
19. H.-O. Walther, A theorem on the amplitudes of periodic solutions of differential delay equations with applications to bifurcation, J. Differential Equations 29 (1978) 396-404.
20. E.M. Wright, A non-linear difference-differential equation, J. Reine Angew. Math. 194 (1955) 66-87.
21. T. Yoneyama, On the 3/2 stability theorem for one-dimensional delay-differential equation, J. Math. Anal. Appl. 125 (1987) 161-173.
22. T. Yoneyama, The 3/2 stability theorem for one-dimensional delay-differential equation with unbounded delay, J. Math. Anal. Appl. 165 (1992) 133-143.
23. J.A. Yorke, Asymptotic stability for one dimensional delay-differential equations, J. Differential Equations 7 (1970) 189-202.