Abstract
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.
References
[1] S. Elaydi, Discrete Chaos: With Applications in Science and Engineering, Second Edition, (Chapman & Hall/CRC, 2008) 10.1201/9781420011043Search in Google Scholar
[2] M.P. Hassell, Host-parasitoid population dynamics, Journal of Animal Ecology, (2000), 69,543-566. 10.1046/j.1365-2656.2000.00445.xSearch in Google Scholar
[3] M.P. Hassell, R.M. May, Aggregation in predators and insect parasites and its effect on stability. (1974),J. Anim. Ecol. 43, 567–594. Search in Google Scholar
[4] M.P. Hassell, R.M.May, Spatial heterogeneity and the dynamics of parasitoid–host systems, 1988. Ann. Zool. Fenn. 25, 55–62. Search in Google Scholar
[5] M.P. Hassell, S.W. Pacala, 1990. Heterogeneity and the dynamics of host–parasitoid interactions. Philos. Trans. R. Soc. London B: Biol. Sci. 330, 203–220. 10.1098/rstb.1990.0193Search in Google Scholar
[6] A.N.W Hone, M.V. Irle, and G.W. Thurura, On the Neimark– Sacker bifurcation in a discrete predator-prey system, Journal of Biological Dynamics, (2010), vol. 4(6), pp. 594–606. Search in Google Scholar
[7] S.R.-J. Jang and S.L. Diamond, A host-parasitoid interactionwith Allee effects on the host, Computers and Mathematics with Applications, (2007), vol. 53, pp. 89–103. Search in Google Scholar
[8] S. Kapçak, U. Ufuktepe, S. Elaydi, Stability and invariant manifolds of a generalized Beddington host-parasitoid model, (2013), Journal of biological dynamics 7 (1), 233-253. 10.1080/17513758.2013.849764Search in Google Scholar PubMed
[9] R.M. May, 1978. Host–parasitoid systems in patchy environments: a phenomenological model. J. Anim. Ecol. 47, 833–843. 10.2307/3674Search in Google Scholar
[10] A.J. Nicholson and V.A. Bailey, The Balance of Animal Population-Part 1, Proceedings of the Zoological Society of London Issue 3, Volume 105, (1935), pp. 551–598, DOI:10.1111/j.1096-3642.1935.tb01680 Search in Google Scholar
©2015 U. Ufuktepe and S. Kapcak
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