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.
[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]