A. Q. Khan M. Askari H. S. Alayachi M. S. M. Noorani Department of Mathematics, University of Azad Jammu and Kashmir, Muzaffarabad 13100, Pakistan School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia Computational Ecology and Software ISSN 2220-721X http://www.iaees.org/publications/journals/ces/online-version.asp 2020 10 1 15 43 International Academy of Ecology and Environmental Sciences Hong Kong 19 November 2019 25 December 2019 1 March 2020 Beddington model stability and bifurcation Allee effect numerical simulation We explore thelocal dynamical properties and supercritical N-S bifurcation of the following Beddington model with Allee effect in R2+: xt+1=xt exp(r(1-xt)-yt), yt+1=m xt (1-exp(-yt)) yt/(B+yt), where xt (respectively yt) denotes densities of host (respectively parasitoid) at time t, r and m respectively denotes number of eggs laid by host and parasitoid which survive through larvae, pupae, and adult stages, and B is constant. More specifically, we explored that model has three equilibria namely the trivial, boundary and positive equilibrium point. We studied the local dynamics along with topological classification about equilibria of the under consideration model. We also explored the existence of bifurcation about equilibria of the model. It is proved about boundary equilibrium point parasitoidgoes to extinction whilehost population undergoes a flip bifurcation to chaos by taking r as bifurcation parameter. It is explored that aboutpositive equilibrium point, model undergoes N-S bifurcation and in meantime invariant closed curve appears. In the perspective of the biology, these curves correspond to periodic or quasi-periodic oscillations between host and parasitoid populations. Finally theoretical results are verified numerically. http://www.iaees.org/publications/journals/ces/articles/2020-10(1)/discrete-time-host-parasitoid-model-with-Allee-effect.pdf