Searching predator and prey dominance in discrete predator-prey systems with dispersion

SIAM Journal on Applied Mathematics

Volumn 61, Issue 3, 2000, Pages 870-888

  Yakubu, Abdul Aziz ^a,b  

^a HOWARD UNIVERSITY   (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

Dominance; Patches; Predator; Prey; Searching; limit set

Indexed keywords

BIFURCATION (MATHEMATICS); ECOLOGY; GROWTH KINETICS; MATHEMATICAL MODELS; STATISTICAL METHODS;

DISCRETE PREDATOR-PREY SYSTEMS; HOPF DYNAMICS; PATCHES; PREY DOMINANCE; SEARCHING PREDATORS;

COMPUTER SIMULATION;

EID: 0034917644     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139999346422     Document Type: Article

References (22)

1. H.N. COMINS AND M.P. HASSELL, Predation in multi-prey communities, J. Theoret. Biol., 62 (1976), pp. 93-114.
2. J. FRANKE AND A. YAKUBU, Diffusion between patches in multi-species discrete competitive systems, in Advances in Difference Equations, S. Elaydi, G. Ladas, and I. Gyori, eds., Gordon and Breach, Amsterdam, 1997, pp. 205-212.
3. J. FRANKE AND A. YAKUDU, Extinction and persistence of species in discrete competitive systems with a safe refuge, J. Math. Anal., 203 (1996), pp. 746-761.
4. J. FRANKE AND A. YAKUBU, Global attractors in competitive systems, Nonlinear Anal., 16 (1991), pp. 111-129.
5. J. FRANKE AND A. YAKUBU, Mutual exclusion versus coexistence in discrete competitive systems, J. Math. Biol., 30 (1990), pp. 161-168.
6. M.P. HASSELL, The Dynamics of Competition and Predation, Stud. Biol. 72, Edward Arnold Publishers, London, 1976.
7. M.P. HASSELL AND R.M. MAY, Aggregation of predators and insect parasites and its effect on stability, J. Anim. Ecol., 43 (1974), pp. 567-594.
8. A. HASTINGS, Complex interactions between dispersal and dynamics: Lessons from coupled logistic equations, Ecology, 74 (1993), pp. 1362-1372.
9. S.A. LEVIN, Dispersion and population interactions, Amer. Nat., 108 (1974), pp. 207-228.
10. Z. LU AND Y. TAKEUCHI, Global asymptotic behavior in a single-species discrete diffusion system, J. Math. Biol., 32 (1993), pp. 67-77.
11. R.M. MAY, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, NJ, 1975.
12. C. MEIER, W. SENN, AND M. ZIMMERMANN, Strange limits of stability in host-parasitoid systems, J. Math. Biol., 32 (1994), pp. 563-572.
13. A.J. NICHOLSON AND V.A. BAILEY, The balance of animal populations, Proc. Zoological Soc. Lond., 551 (1935), pp. 551-598.
14. R.T. PAINE, Food web complexity and species diversity, Amer. Nat., 100 (1966), pp. 65-75.
15. R.T. PAINE, Intertidal community structure experimental studies on the relationship between a dominant competitor and its principal predator, Oecologia, 15 (1974), pp. 92-120.
16. T. ROYAMA, Factors governing the hunting behaviour and selection of food by the great tit, J. Anim. Ecol., 39 (1970), pp. 619-668.
17. J.F. SELGRADE AND G. NAMKOONG, Stable periodic behavior in a pioneer-climax model, Natural Resource Modelling, 4 (1990), pp. 215-227.
18. L. TINBERGEN, The natural control of insects in pinewoods. I. Factors influencing the intensity of predation by songbirds, Arch. Néerl. Zool., 13 (1960), pp. 266-336.
19. Y. TAKEUCHI, Diffusion-Mediated persistence in three-species competition models with heteroclinic cycles, Math. Biosci., 106 (1991), pp. 111-128.
20. Y. TAKEUCHI, Global stability in generalized Lotka-Volterra diffusion systems, J. Math. Anal. Appl., 116 (1986), pp. 209-221.
21. Y. TAKEUCHI, Refuge mediated coexistence of multiple competitors on.a single resource, in Recent Trends in Differential Equations, R.P. Agarwal, ed., World Scientific, River Edge, NJ, 1992, pp. 531-541.
22. A. YAKUBU, Prey dominance in discrete predator-prey systems with a prey refuge, Math. Biosci., 144 (1997), pp. 155-178.