title: Global dynamics and bifurcation analysis of a host-parasitoid model with strong Allee effect.
abstract: In this paper, we study the global dynamics and bifurcations of a two-dimensional discrete time host-parasitoid model with strong Allee effect. The existence of fixed points and their stability are analysed in all allowed parametric region. The bifurcation analysis shows that the model can undergo fold bifurcation and Neimark-Sacker bifurcation. As the parameters vary in a small neighbourhood of the Neimark-Sacker bifurcation condition, the unique positive fixed point changes its stability and an invariant closed circle bifurcates from the positive fixed point. From the viewpoint of biology, the invariant closed curve corresponds to the periodic or quasi-periodic oscillations between host and parasitoid populations. Furthermore, it is proved that all solutions of this model are bounded, and there exist some values of the parameters such that the model has a global attractor. These theoretical results reveal the complex dynamics of the present model.
authors.affiliation: a Department of Mathematics , University of Azad Jammu & Kashmir , Muzaffarabad , Pakistan.
authors.forename: Abdul Qadeer
authors.initials: AQ
authors.lastname: Khan
authors.affiliation: b College of Science , University of Shanghai for Science and Technology , Shanghai , People's Republic of China.
authors.forename: Jiying
authors.initials: J
authors.lastname: Ma
authors.affiliation: c Department of Mathematics , Shanghai Jiao Tong University , Shanghai , People's Republic of China.
authors.forename: Dongmei
authors.initials: D
authors.lastname: Xiao
mesh_terms: D006790:Host-Parasite Interactions; D008954:Models, Biological; D011157:Population Dynamics
keywords: 34K20; 39A10; 40A05; 92C50; Allee effect; Host–parasitoid model; attractor; bifurcations; fixed points