Ratio-dependent predator-prey models of interacting populations

Bulletin of Mathematical Biology

Volumn 71, Issue 2, 2009, Pages 430-452

  Haque, Mainul ^a  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

Bifurcation; Competition among predators; Paradox of enrichment; Permanence; Predator prey; Ratio dependence; Stability

Indexed keywords

ANIMAL; ARTICLE; COMPETITIVE BEHAVIOR; ECOSYSTEM; POPULATION DENSITY; POPULATION DYNAMICS; POPULATION MIGRATION; PREDATION; SYSTEMS THEORY; THEORETICAL MODEL; TIME;

ANIMAL MIGRATION; ANIMALS; COMPETITIVE BEHAVIOR; ECOSYSTEM; MODELS, THEORETICAL; POPULATION DENSITY; POPULATION DYNAMICS; PREDATORY BEHAVIOR; SYSTEMS THEORY; TIME FACTORS;

EID: 58349121665     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-008-9368-4     Document Type: Article

References (31)

1. P.A. Abrams 1994 The fallacies of 'Ratio-dependent' predation Ecology 75 6 1842 1850
2. H.R. Akcakaya R. Arditi L.R. Gingburg 1995 Ratio-dependent predation: an abstraction that works Ecology 76 995 1004
3. V.V. Alekseev 1973 Effect of saturation factor on dynamics of predator prey system Biofizika 18 922 926
4. D. Alonso F. Bartumeus J. Catalan 2002 Mutual interference between predators can give rise to Turing spatial Patterns Ecology 83 1 28 34
5. R. Arditi L.R. Ginzburg 1989 Coupling in predator-prey dynamics: ratio-dependence J. Theor. Biol. 139 311 326
6. O. Arino J. Mikram J. Chattopadhyay 2004 Infection on prey population may act as a biological control in ratio-dependent predator-prey model Nonlinearity 17 1101 1116
7. Bazykin, A.D., 1998. Nonlinear Dynamics of Interacting Populations. Series on Nonlinear Science. Ser. A, vol. 11. World Scientific, Singapore. Chua, L.O. (Ed.), Original Russian version: Bazykin, A.D. Nauka, Moscow (1985).
8. F. Berezovskaya G. Karev R. Arditi 2001 Parametric analysis of ratio-dependent predator-prey model J. Math. Biol. 43 221 246
9. C. Cosner D.L. Angelis J.S. Ault D.B. Olson 1999 Effects of spatial grouping on the functional response of predators Theor. Popul. Biol. 56 65 75
10. Freedman, H.I., 1980. Deterministic Mathematical Method in Population Ecology. Dekker, New York.
11. W.M. Getz 1984 Population dynamics-a per capita resource approach J. Theor. Biol. 108 623 643
12. D. Greenhalgh M. Haque 2007 A predator-prey model with disease in the prey species only Math. Methods Appl. Sci. 30 911 929
13. A.P. Gutierrez 1992 The physiological basis of ratio-dependent predator-prey theory: a metabolic pool model of Nicholson's blowflies as an example Ecology 73 1552 1563
14. Hale, J., 1969. Ordinary Differential Equations. Wiley-Interscience, New York.
15. I. Hanski 1991 The functional response of predator: worries about scale TREE 6 141 142
16. M. Haque E. Venturino 2007 An eco-epidemiological model with disease in predator: the ratio-dependent case Math. Methods Appl. Sci. 30 1791 1809
17. S.B. Hsu T.W. Hwang Y. Kuang 2001 Rich dynamics of ratio-dependent one prey two predators model J. Math. Biol. 43 377 396
18. S.B. Hsu T.W. Hwang Y. Kuang 2001 Global analysis of the Michaelis Menten type ratio-dependent predator-prey system J. Math. Biol. 42 489 506
19. S.B. Hsu T.W. Hwang Y. Kuang 2003 A ratio-dependent food chain model and its application to biological control Math. Biosci. 181 55 83
20. C. Jost R. Arditi 2000 Identifying predator-prey process from time series Theor. Popul. Biol. 57 325 337
21. C. Jost O. Arino R. Arditi 1999 About deterministic extinction in ratio-dependent predator-prey models Bull. Math. Biol. 61 19 32
22. Y. Kuang 1999 Rich dynamics of Gause-type ratio-dependent predator-prey system Fields Inst. Commun. 21 325 337
23. Y. Kuang E. Bertta 1998 Global qualitative analysis of a ratio-dependent predator-prey system J. Math. Biol. 36 389 406
24. L.S. Luckinbill 1973 Coexistence in laboratory populations of Paramecium Aurelia and its predator Didinium nasutum Ecology 54 1320 1327
25. May, R.M., 1974. Stability and Complexity in Model Eco-System. Princeton University Press, Princeton.
26. Murray, J.D., 1989. Mathematical Biology. Biomathematics, vol. 19. Springer, Berlin.
27. J.T. Tanner 1975 The stability and intrinsic growth rates of prey and predator populations Ecology 56 855 867
28. Thieme, H., 1997. Mathematical Biology. An Introduction via Selected Topics. Lecture Note at Arizona State University.
29. Sotomayor, J., 1973. Generic bifurcation of dynamical systems. In: Peixoto, M.M. (Ed.), Dynamical System. Academic Press, San Diego.
30. D. Xiao S. Ruan 2001 Global dynamics of ratio-dependent predator-prey system J. Math. Biol. 43 268
31. Y. Xiao L. Chen 2002 A ratio-dependent predator-prey model with disease in the prey Appl. Math. Comput. Arch. 131 397 414