Generalized Beddington model with the host subject to the Allee Effect

• Autorzy: U. Ufuktepe , S. Kapcak
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

host-parasitoid; predator-prey; beddingtonmodel; allee effect; discrete dynamical systems

• Czasopismo: Open Physics
• Rocznik: 2015
• Tom: 13
• Numer: 1

Daty

otrzymano

2015-08-13

zaakceptowano

2015-12-01

online

2015-12-31

Twórcy

autor

U. Ufuktepe

• American University of the Middle East, Department of Mathematics & Statictics, Egaila, Kuwait

autor

S. Kapcak

• American University of the Middle East, Egaila, Kuwait

Bibliografia

• [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]

Identyfikatory

DOI

10.1515/phys-2015-0055