Permanence in delayed ratio-dependent predator-prey models with monotonic functional responses

Nonlinear Analysis: Real World Applications

Volumn 8, Issue 2, 2007, Pages 424-434

  Fan, Yong Hong ^a,b   Li, Wan Tong ^b  

^a NORTHWEST NORMAL UNIVERSITY   (China)

^b LANZHOU UNIVERSITY   (China)

Author keywords

Monotonic response functional; Permanence; Predator prey model; Ratio dependent

Indexed keywords

FUNCTIONS; SYSTEMS ANALYSIS;

MONOTONIC RESPONSE FUNCTIONALS; PERMANENCE; PREDATOR-PREY MODELS; RATIO-DEPENDENT MODELS;

MATHEMATICAL MODELS;

EID: 33845565942     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2005.12.003     Document Type: Article

References (20)

1. Arditi R., and Saiah H. Empirical evidence of the role of heterogeneity in ratio-dependent consumption. Ecology 73 (1992) 1544-1551
2. Beretta E., and Kuang Y. Global analysis in some delayed ratio-dependent predator-prey systems. Nonlinear Anal. TMA 32 (1998) 381-408
3. Berryman A.A. The origins and evolution of predator-prey theory. Ecology 75 (1992) 1530-1535
4. Fan M., and Wang K. Periodicity in a delayed ratio-dependent predator-prey system. J. Math. Anal. Appl. 262 (2001) 179-190
5. Fan Y.H., Li W.T., and Wang L.L. Periodic solutions in delayed ratio-dependent predator-prey models with monotonic or nonmonotonic functional responses. Nonlinear Anal. RWA 5 (2004) 247-263
6. Freedman H.I., and Ruan S.G. Uniform persistence in functional differential equations. J. Differential Equations 115 (1995) 173-192
7. Freedman H.I., and Wu J. Persistence and global asymptotical stability of single species dispersal models with stage structure. Quart. Appl. Math. Appl. 49 (1991) 351-371
8. Gutierrez A.P. The physiological basis of ratio-dependent predator-prey theory: a metabolic pool model of Nicholson's blowflies as an example. Ecology 73 (1992) 1552-1563
9. Hale J.K., and Waltman P. Persistence in infinite-dimensional systems. SIAM J. Math. Anal. 20 (1989) 388-395
10. Hsu S.B., Hwang T.W., and Kuang Y. Global analysis of the Michaelis-Menten type ratio-dependent predator-prey system. J. Math. Biol. 42 (2001) 489-506
11. Jost C., Arino O., and Arditi R. About deterministic extinction in ratio-dependent predator-prey models. Bull. Math. Biol. 61 (1999) 19-32
12. Kuang Y., and Beretta E. Global qualitative analysis of a ratio-dependent predator-prey system. J. Math. Biol. 36 (1998) 389-406
13. Liu S., and Chen L. Persistence, extinction and balancing survival in nonautonomous Lotka-Volterra system with delays. Appl. Math. Comput. 129 (2002) 481-499
14. Lu Z., and Takeuchi Y. Permanence and global attractivity for competitive Lotka-Volterra systems with delay. Nonlinear Anal. 22 (1994) 847-856
15. Saito Y. Permanence and global stability for general Lotka-Volterra predator-prey systems with distributed delays. Nonlinear Anal. 47 (2001) 6157-6168
16. Saito Y., Hara T., and Ma W. Necessary and sufficient conditions for permanence and global stability of a Lotka-Volterra system with two delays. J. Math. Anal. Appl. 236 (1999) 534-556
17. Smith H.I. Monotone semiflows generated by functional differential equations. J. Differential Equations 66 (1987) 420-442
18. Waltman P. A brief survey of persistence in dynamical systems. In: Busenberg S., and Martelli M. (Eds). Delayed Differential Equations and Dynamical Systems (1991), Springer, Berlin 31-40
19. Wang L.L., and Li W.T. Existence and global stability of positive periodic solutions of a predator-prey system with delays. Appl. Math. Comput. 146 (2003) 167-185
20. Wang W., and Ma E. Harmless delays for uniform persistence. J. Math. Anal. Appl. 158 (1991) 256-268