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Journal
2015 | 13 | 1 |
Article title

Generalized Beddington model with the host
subject to the Allee Effect

Content
Title variants
Languages of publication
EN
Abstracts
EN
We investigate the stability and invariant manifolds
of generalized Beddington model with the host population
subject to the Allee effect.We obtain the condition
for the existence of the fixed points and investigate the stability
of the system.
Publisher

Journal
Year
Volume
13
Issue
1
Physical description
Dates
accepted
1 - 12 - 2015
received
13 - 8 - 2015
online
31 - 12 - 2015
Contributors
author
  • American University of the Middle East, Department of Mathematics & Statictics, Egaila, Kuwait
author
  • American University of the Middle East, Egaila, Kuwait
References
  • [1] S. Elaydi, Discrete Chaos: With Applications in Science and Engineering,Second Edition, (Chapman & Hall/CRC, 2008)
  • [2] M.P. Hassell, Host-parasitoid population dynamics, Journal ofAnimal Ecology, (2000), 69,543-566.
  • [3] M.P. Hassell, R.M. May, Aggregation in predators and insectparasites and its effect on stability. (1974),J. Anim. Ecol. 43,567–594.
  • [4] M.P. Hassell, R.M.May, Spatial heterogeneity and the dynamicsof parasitoid–host systems, 1988. Ann. Zool. Fenn. 25, 55–62.
  • [5] M.P. Hassell, S.W. Pacala, 1990. Heterogeneity and the dynamicsof host–parasitoid interactions. Philos. Trans. R. Soc. LondonB: Biol. Sci. 330, 203–220.
  • [6] A.N.W Hone, M.V. Irle, and G.W. Thurura, On the Neimark–Sacker bifurcation in a discrete predator-prey system, Journalof Biological Dynamics, (2010), vol. 4(6), pp. 594–606.
  • [7] S.R.-J. Jang and S.L. Diamond, A host-parasitoid interactionwithAllee effects on the host, Computers and Mathematics with Applications,(2007), vol. 53, pp. 89–103.
  • [8] S. Kapçak, U. Ufuktepe, S. Elaydi, Stability and invariant manifoldsof a generalized Beddington host-parasitoid model,(2013), Journal of biological dynamics 7 (1), 233-253.
  • [9] R.M. May, 1978. Host–parasitoid systems in patchy environments:a phenomenological model. J. Anim. Ecol. 47, 833–843.
  • [10] A.J. Nicholson and V.A. Bailey, The Balance of AnimalPopulation-Part 1, Proceedings of the Zoological Societyof London Issue 3, Volume 105, (1935), pp. 551–598,DOI:10.1111/j.1096-3642.1935.tb01680[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_1515_phys-2015-0055
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