Bifurcation analysis of a predator-prey model with predators using hawk and dove tactics

Journal of Theoretical Biology

Volumn 238, Issue 3, 2006, Pages 597-607

  Auger, Pierre ^a   Kooi, Bob W ^b   Bravo De La Parra, Rafael ^c   Poggiale, Jean Christophe ^d  

^a INSTITUT DE RECHERCHE POUR LE DÉVELOPPEMENT   (France)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

^c UNIVERSITY OF ALCALÁ   (Spain)

^d STATION MARINE D ENDOUME   (France)

Author keywords

Aggregation of variables; Bifurcation analysis; Hawk dove tactics; Predator prey model; Slow fast dynamics

Indexed keywords

BEHAVIOR; BIFURCATION; PREDATOR-PREY INTERACTION;

ANIMAL BEHAVIOR; ARTICLE; BIOLOGICAL MODEL; BIOMASS; DOVE; HAWK; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; NONHUMAN; POPULATION DYNAMICS; PREDATION; PREDATOR PREY INTERACTION; PRIORITY JOURNAL;

ANIMALS; GAME THEORY; MODELS, PSYCHOLOGICAL; PREDATORY BEHAVIOR;

ANIMALIA;

EID: 30444445111     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2005.06.012     Document Type: Article

References (36)

1. P. Auger, and R. Bravo de la Parra Methods of aggregation of variables in population dynamics Comptes rendus de l'Academie des science series III-Sciences de la vie-life 323 2000 665 674
2. P. Auger, and J.C. Poggiale Aggregation and emergence in systems of ordinary differential equations Math. Comput. Model. 27 4 1998 1 21
3. P. Auger, and D. Pontier Fast game theory coupled to slow population dynamics: the case of domestic cat populations Math. Biosci. 148 1998 65 82
4. P. Auger, R. Bravo de la Parra, S. Morand, and E. Sánchez A predator-prey model with predators using hawk and dove tactics Math. Biosci. 177-178 2002 185 200
5. A.D. Bazykin Nonlinear Dynamics of Interacting Populations 1998 World Scientific Singapore
6. J.R. Beddington Mutual interference between parasites or predators and its effect on searching efficiency J. Anim. Ecol. 44 1975 331 440
7. C. Bernstein, P. Auger, and J.-C. Poggiale Predator migration decisions the ideal free distribution, and predator-prey dynamics Am. Nat. 153 1999 267 281
8. R. Bravo de la Parra, P. Auger, and E. Sanchez Aggregation methods in discrete models J. Biol. Syst. 3 1995 603 612
9. K.-S. Cheng Uniqueness of a limit cycle for predator-prey system SIAM J. Math. Anal. 12 1981 541 548
10. E.A. Coddington, and N. Levinson Theory of Ordinary Differential Equations 1955 McGraw-Hill New York
11. D.L. DeAngelis, R.A. Goldstein, and R.V. O'Neill A model for trophic interaction Ecology 56 4 1975 881 892
12. Doedel, E. J., Champneys, A. R., Fairgrieve, T. F., Kuznetsov, Y. A., Sandstede, B., Wang, X. (1997). Auto 97: Continuation and bifurcation software for ordinary differential equations. Technical report, Concordia University, Montreal, Canada.
13. H. Gintis Game Theory Evolving: A Problem-Centered Introduction to Modeling Strategic Behaviour 2000 Princeton University Press Princeton
14. J. Hofbauer, and K. Sigmund Evolutionary Games and Population Dynamics 1998 Cambridge University Press Cambridge
15. S.B. Hsu, S.P. Hubbell, and P. Waltman Competing predators SIAM J. Appl. Math. 35 1978 617 625
16. Y. Iwasa, V. Andreasen, and S.A. Levin Aggregation in model ecosystems I. Perfect aggregation Ecol. Model. 37 1987 287 302
17. Y. Iwasa, S.A. Levin, and V. Andreasen Aggregation in model ecosystems II. Approximate aggregation IMA J. Math. Appl. Med. Biol. 6 1989 1 23
18. A.I. Khibnik, Y.A. Kuznetsov, V.V. Levitin, and E.V. Nikolaev Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps Physica D 62 1993 360 371
19. B.W. Kooi, M.P. Boer, and S.A.L.M. Kooijman Mass balance equation versus logistic equation in food chains J. Biol. Syst. 5 1 1997 77 85
20. B.W. Kooi, J.C. Poggiale, and P. Auger Aggregation methods in food chains Math. Comput. Model. 27 4 1998 109 120
21. B.W. Kooi, M.P. Boer, and S.A.L.M. Kooijman On the use of the logistic equation in food chains Bull. Math. Biol. 60 2 1998 231 246
22. B.W. Kooi, J.C. Poggiale, P. Auger, and S.A.L.M. Kooijman Aggregation methods in food chains with nutrient recycling Ecol. Model. 157 1 2002 69 86
23. Kuznetsov, Y.A., 1998. Elements of Applied Bifurcation Theory, Vol. 112 of Applied Mathematical Sciences, second ed. Springer, New York.
24. Liberg, O., 1981. Predation and social behaviour in a population of domestic cats: an evolutionary perspective. Ph.D. thesis, University of Lund.
25. O. Liberg, and M. Sandell Spatial organization and reproductive tactics in the domestic cat and other fields D.C. Turner P. Bateson The Domestic Cat 1988 Cambridge University
26. D.F. Lott Intraspecific Variation in the Social Systems of Wild Vertebrates 1991 Cambridge University New York
27. F.C. Neat, F.A. Huntingford, and M.M.C. Beveridge Fighting and assessment in male ciclid fish: the effects of asymmetries in gonadal state and body size Anim. Behav. 55 1998 883 891
28. F.C. Neat, A.C. Taylor, and F.A. Huntingford Proximate costs of fighting in male ciclid fish: the role of injuries and energy metabolism Anim. Behav. 55 1998 875 882
29. P. Perret, and J. Blondel Experimental evidence of the territorial defense hypothesis in insular blue tits Experientia 49 1 1993 94 98
30. D. Pontier, N. Rioux, and A. Heizmann Evidence of selection on the orange allele in the domestic cat Felis catus - The role of social-structure Oikos 73 3 1995 299 308
31. D. Pontier, P. Auger, R. Bravo de la Parra, and E. Sanchez The impact of behavioral plasticity at individual level on domestic cat population dynamics Ecol. Model. 133 2000 117 124
32. M.L. Rosenzweig Paradox of enrichment: destabilization of exploitation ecosystems in ecological time Science 171 1971 385 387
33. K. Sakamoto Invariant manifolds in singular perturbation problems for ordinary differential equations Proc. R. Soc. Edin. A-Mathematics 116 1990 45 78
34. J.A. Stamps, and M. Buechner The territorial defense hypothesis and the ecology of insular vertebrates Q. Rev. Biol. 60 2 1985 155 181
35. L.L. Wolf, and E. Waltz Alternative mating tactics in male white-faced dragonflies: Experimental evidence for a behavioural assessment ess Anim. Behav. 46 1993 325 334
36. A. Yamane, T. Doi, and Y. Ono Mating behaviors, courtship rank and mating success of male feral cat (Felis catus) J. Ethol. 14 1996 35 44