Dynamic complexity and bifurcation analysis of a host–parasitoid model with Allee effect and Holling type III functional response

In this paper, we focus on dynamics in a basic discrete-time system of host–parasitoid interaction. We perform local stability analysis of this system. Furthermore, both flip and Neimark–Sacker bifurcations are also analyzed in the interior of R+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R_{ +}^{2}$\end{document} by using center manifold theorem and bifurcation theory. Finally, numerical simulations are deployed to validate our results with theoretical analysis and to exhibit the dynamical behaviors.