Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure

Journal of Mathematical Analysis and Applications

Volumn 303, Issue 2, 2005, Pages 602-621

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

^a MECHANICAL ENGINEERING COLLEGE   (China)

^b UNIVERSITY OF DUNDEE   (United Kingdom)

Author keywords

Periodic solution; Permanence; Ratio dependence; Stage structure; Time delay

Indexed keywords

EID: 13844265911     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2004.08.062     Document Type: Article

References (37)

1. W.G. Aiello H.I. Freedman A time delay model of single-species growth with stage structure Math. Biosci. 101 1990 139-153
2. W.G. Aiello H.I. Freedman J. Wu Analysis of a model representing stage-structured population growth with state-dependent time delay SIAM J. Appl. Math. 52 1992 855-869
3. R. Arditi L.R. Ginzburg Coupling in predator-prey dynamics: ratio-dependence J. Theor. Biol. 139 1989 311-326
4. R. Arditi L.R. Ginzburg H.R. Akcakaya Variation in plankton densities among lakes: A case for ratio-dependent models Amer. Naturalists 138 1991 1287-1296
5. R. Arditi N. Perrin H. Saiah Functional response and heterogeneities: An experiment test with cladocerans OIKOS 60 1991 69-75
6. R. Arditi H. Saiah Empirical evidence of the role of heterogeneity in ratio-dependent consumption Ecology 73 1992 1544-1551
7. J.R. Bence R.M. Nisbet Space-limited recruitment in open system: The importance of time delays Ecology 70 1989 1434-1441
8. E. Beretta Y. Kuang Global analyses in some delayed ratio-dependent predator-prey systems Nonlinear Anal. 32 1998 381-408
9. F. Berezovskaya G. Karev R. Arditi Parametric analysis of the ratio-dependent predator-prey model J. Math. Biol. 43 2001 221-246
10. F. Brauer Z. Ma Stability of stage-structured population models J. Math. Anal. Appl. 126 1987 301-315
11. J.M. Cushing Periodic time-dependent predator-prey system SIAM J. Appl. Math. 32 1977 82-95
12. M. Fan K. Wang Periodicity in a delayed ratio-dependent predator-prey system J. Math. Anal. Appl. 262 2001 179-190
13. H.I. Freedman J. Wu Persistence and global asymptotic stability of single species dispersal models with stage structure Quart. Appl. Math. 49 1991 351-371
14. R.E. Gaines J.L. Mawhin Coincidence Degree and Nonlinear Differential Equations 1977 Springer-Verlag Berlin
15. B.S. Goh Global stability in two species interactions J. Math. Biol. 3 1976 313-318
16. A.P. Gutierrez 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
17. J.K. Hale S.M.V. Lunel Introduction to Functional Differential Equations 1993 Springer-Verlag New York
18. I. Hanski The functional response of predator: Worries about scale TREE 6 1991 141-142
19. A. Hastings Global stability in two species systems J. Math. Biol. 5 1978 399-403
20. X. He Stability and delays in a predator-prey system J. Math. Anal. Appl. 198 1996 355-370
21. S.B. Hsu T.W. Hwang Y. Kuang Global analysis of the Michaelis-Menten ratio-dependent predator-prey system J. Math. Biol. 42 2001 489-506
22. S.B. Hsu T.W. Hwang Y. Kuang Rich dynamics of a ratio-dependent one prey two predator model J. Math. Biol. 43 2001 377-396
23. S.B. Hsu T.W. Hwang Y. Kuang A ratio-dependent food chain model and its applications to biological control Math. Biosci. 181 2003 55-83
24. C. Jost O. Arino R. Arditi About deterministic extinction in ratio-dependent predator-prey models Bull. Math. Biol. 61 1999 19-32
25. Y. Kuang E. Beretta Global qualitative analysis of a ratio-dependent predator-prey system J. Math. Biol. 36 1998 389-406
26. Y. Kuang J.W.H. So Analysis of a delayed two-stage population with space-limited recruitment SIAM J. Appl. Math. 55 1995 1675-1695
27. S. Liu L. Chen Z. Liu Extinction and permanence in nonautonomous competitive system with stage structure J. Math. Anal. Appl. 274 2002 667-684
28. S. Liu L. Chen R. Agarwal Recent progress on stage-structured population dynamics Math. Comput. Modelling 36 2002 1319-1360
29. K.G. Magnusson Destabilizing effect of cannibalism on a structured predator-prey system Math. Biosci. 155 1999 61-75
30. X. Song L. Chen Optimal harvesting and stability for a two-species competitive system with stage structure Math. Biosci. 170 2001 173-186
31. X. Song L. Chen Modelling and analysis of a single species system with stage structure and harvesting Math. Comput. Modelling 36 2002 67-82
32. W. Wang L. Chen A predator-prey system with stage structure for predator Comput. Math. Appl. 33 1997 83-91
33. W. Wang G. Mulone F. Salemi V. Salone Permanence and stability of a stage-structured predator-prey model J. Math. Anal. Appl. 262 2001 499-528
34. D. Xiao S. Ruan Global dynamics of a ratio-dependent predator-prey system J. Math. Biol. 43 2001 268-290
35. D. Xiao S. Ruan Stability and bifurcation in a delayed ratio-dependent predator-prey system Proc. Edinburgh Math. Soc. 45 2002 205-220
36. R. Xu L. Chen 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
37. R. Xu L. Chen Persistence and global stability for n-species ratio-dependent predator-prey system with time delays J. Math. Anal. Appl. 275 2002 27-43