Permanence and stability in non-autonomous logistic systems with infinite delay

Dynamical Systems

Volumn 17, Issue 3, 2002, Pages 187-202

  Teng, Zhidong ^a  

^a XINJIANG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; INTEGRAL EQUATIONS; MATHEMATICAL MODELS; SYSTEM STABILITY;

INFINITE DISTRIBUTED DELAY; NONAUTONOMOUS LOGISTIC SYSTEMS; TIME DEPENDENT DISCRETE DELAY;

ASYMPTOTIC STABILITY;

EID: 0036763656     PISSN: 14689367     EISSN: None     Source Type: Journal    
DOI: 10.1080/14689360110102312     Document Type: Article

References (21)

1. Chen, M. P., Yu, J. S., Qian, X. Z., and Wang, Z. C., 1995, On the stability of a delay differential population model. Nonlinear Analysis. 25: 187-195.
2. Coleman, B. D., Ysieh, Y. H., and Knowles, G. P., 1979, On the optimal choice of τ for a population in a periodic environment. Mathematical Biosciences, 46: 71-85.
3. Cushing, J. M., 1977a, Stable positive periodic solutions of the time-dependent logistic equation under possible hereditary influences. Journal of Mathematical Analysis and Applications, 60: 747-754.
4. Cushing, J. M., 1977b, Intergrodifferential Equations and Delay Models in Population Dynamics, Lecture Notes in Biomathematics, Vol. 20 (Berlin: Springer-Verlag).
5. Freedman, H. I., and Wu, J. H., 1992, Periodic solutions of single-species models with periodic delay. SIAM Journal on Mathematical Analysis, 23: 689-701.
6. Gopalsamy, K. Kulenovic, M. R. S., and Ladas, G., 1990 Environment periodicity and time delays in a "food-limited" population model. Journal of Mathematical Analysis and Applications, 147: 545-555.
7. Gopalsamy, K., and Lalli, B. S., 1992 Oscillatory and asymptotic behavior of a multiplicative delay logistic equation. Dynamics and Stability of Systems, 7: 35-42.
8. Gyori, I., 2000, A new approach to the global asymptotic stability problem in a delay Lotka-Voterra differential equation. Mathematical & Computational Modelling, 31, 9-28.
9. Gyori, I., and Pituk, M., 1996, Comparison theorem and asymptotic equilibrium for delay differential and difference equations. Dynamical Systems and Applications, 5: 277-302.
10. He, C. Y., 1992, Almost Periodic Differential Equations (Beijing: Higher Education Publishing House) (in Chinese).
11. Kuang, Y., 1991 Global stability for a class of nonlinear nonautonomous delay equations. Nonlinear Analysis, 17: 627-634.
12. Kuang, Y., 1993, Delay Differential Equations with Applications in Population Dynamics (Boston: Academic Press).
13. Kuang, Y., Zhang, B. G., and Zhao, T., 1991, Qualitative analysis of nonautonomous non-linear delay differential equation. Tohoku Mathematical Journal, 43: 509-528.
14. Makay, G., 1995, Periodic solutions of linear differential and integral equations. Differential and Integral Equations, 8: 2177-2187.
15. Makay, G., 1996, Periodic solutions of dissipative functional differential equations with infinite delay. Tohoku Mathematical Journal, 48: 355-362.
16. Seifert, G., 1981, Almost periodic solutions for delay-differential equations with infinite delays. Journal of Differential Equations, 41: 416-425.
17. Seifert, G., 1996, Almost periodic solutions for delay logistic equations with almost periodic time dependence. Differential and Integral Equations, 9: 335-342.
18. Teng, Z., and Chen, L., 1999, Uniform persistence and existence of strictly positive solutions in nonautonomous Lotka-Voltera competitive systems with delays. Computers & Mathematical Applications, 37: 61-71.
19. Vance, R. R., and Coddington, E. A., 1989, A nonautonomous model of population growth. Journal of Mathematical Biology, 27: 495-506.
20. Yuan, R., and Hong, J., 1996, The existence of almost periodic solution of a population equation with delay. Applicable Analysis, 61: 45-52.
21. Zhang, G. G., and Gopalsamy, K., 1990, Global attractivity and oscillations in a periodic delay-logistic equation. Journal of Mathematical Analysis and Applications, 150: 274-283.