Persistence and global stability of a ratio-dependent predator-prey model with stage structure

Applied Mathematics and Computation

Volumn 158, Issue 3, 2004, Pages 729-744

  Xu, Rui ^a,b   Chaplain, M A J ^a   Davidson, F A ^a  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

^b MECHANICAL ENGINEERING COLLEGE   (China)

Author keywords

Global stability; Predator prey model; Ratio dependence; Stage structure; Uniform persistence

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; FUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; POPULATION STATISTICS;

GLOBAL STABILITY; RATIO DEPENDENCE; STAGE STRUCTURES; UNIFORM PERSISTENCE;

PROBLEM SOLVING;

EID: 4944222203     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.10.012     Document Type: Article

References (30)

1. Arditi R., Saiah H. Empirical evidence of the role of heterogeneity in ratio-dependent consumption. Ecology. 73:1992;1544-1551.
2. Arditi R., Ginzburg L.R., Akcakaya H.R. Variation in plankton densities among lakes: a case for ratio-dependent models. American Nat. 138:1991;1287-1296.
3. Arditi R., Perrin N., Saiah H. Functional response and heterogeneities: an experiment test with cladocerans. OIKOS. 60:1991;69-75.
4. Gutierrez A.P. The physiological basis of ratio-dependent predator-prey theory: a methbolic pool model of Nicholson's blowflies as an example. Ecology. 73:1992;1552-1563.
5. Arditi R., Ginzburg L.R. Coupling in predator-prey dynamics: ratio-dependence. J. Theor. Biol. 139:1989;311-326.
6. Hanski I. The functional response of predator: worries bout scale. TREE. 6:1991;141-142.
7. Beretta E., Kuang Y. Global analyses in some delayed ratio-dependent predator-prey systems. Nonlinear Anal. 32:1998;381-408.
8. Berezovskaya F., Karev G., Arditi R. Parametric analysis of the ratio-dependent predator-prey model. J. Math. Biol. 43:2001;221-246.
9. Fan M., Wang K. Periodicity in a delayed ratio-dependent predator-prey system. J. Math. Anal. Appl. 262:2001;179-190.
10. Hsu S.B., Hwang T.W., Kuang Y. Global analysis of the Michaelis-Menten ratio-dependent predator-prey system. J. Math. Biol. 42:2001;489-506.
11. Hsu S.B., Hwang T.W., Kuang Y. Rich dynamics of a ratio-dependent one prey two predator model. J. Math. Biol. 43:2001;377-396.
12. Jost C., Arino O., Arditi R. About deterministic extinction in ratio-dependent predator-prey models. Bull. Math. Biol. 61:1999;19-32.
13. Kuang Y., Beretta E. Global qualitative analysis of a ratio-dependent predator-prey system. J. Math. Biol. 36:1998;389-406.
14. Xiao D., Ruan S. Global dynamics of a ratio-dependent predator-prey system. J. Math. Biol. 43:2001;268-290.
15. Xiao D., Ruan S. Stability and bifurcation in a delayed ratio-dependent predator-prey system. Proc. Edin. Math. Soc. 45:2002;205-220.
16. Xu R., Chen L. Persistence and stability for a two-species ratio-dependent predator-prey system with time delay in a two-patch environment. Comput. Math. Appl. 40:2000;577-588.
17. Xu R., Chen L. Persistence and global stability for. n -species ratio-dependent predator-prey system with time delays J. Math. Anal. Appl. 275:2002;27-43.
18. Aiello W.G., Freedman H.I. A time delay model of single-species growth with stage structure. Math. Biosci. 101:1990;139-153.
19. Aiello W.G., Freedman H.I., Wu J. Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J. Appl. Math. 52:1992;855-869.
20. Brauer F., Ma Z. Stability of stage-structured population models. J. Math. Anal. Appl. 126:1987;301-315.
21. Freedman H.I., Wu J. Persistence and global asymptotic stability of single species dispersal models with stage structure. Quart. Appl. Math. 49:1991;351-371.
22. Kuang Y., So J.W.H. Analysis of a delayed two-stage population with space-limited recruitment. SIAM J. Appl. Math. 55:1995;1675-1695.
23. Liu S., Chen L., Liu Z. Extinction and permanence in nonautonomous competitive system with stage structure. J. Math. Anal. Appl. 274:2002;667-684.
24. Liu S., Chen L., Agarwal R. Recent progress on stage-structured population dynamics. Math. Comput. Model. 36:2002;1319-1360.
25. Magnusson K.G. Destabilizing effect of cannibalism on a structured predator-prey system. Math. Biosci. 155:1999;61-75.
26. Song X., Chen L. Optimal harvesting and stability for a two-species competitive system with stage structure. Math. Biosci. 170:2001;173-186.
27. Wang W., Chen L. A predator-prey system with stage structure for predator. Comput. Math. Appl. 33:1997;83-91.
28. Wang W., Mulone G., Salemi F., Salone V. Permanence and stability of a stage-structured predator-prey model. J. Math. Anal. Appl. 262:2001;499-528.
29. Zhang X., Chen L. The stage-structured predator-prey model and optimal harvesting policy. Math. Biosci. 168:2000;201-210.
30. Gopalsamy K. Stability and Oscillations in Delay Differential Equations of Population Dynamics. 1992;Kluwer Academic, Dordrecht/ Norwell, MA.