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has been cited by the following article:

• TITLE: Local Stability Analysis and Bifurcations of a Discrete-Time Host-Parasitoid Model

  AUTHORS: Tahmineh Azizi

  KEYWORDS: Chaos, Neimark-Sacker Bifurcation, Period-Doubling Bifurcations, Manifold, Saddle-Node Bifurcation

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.9 No.2, June 10, 2020

  ABSTRACT: In this paper, we examine a discrete-time Host-Parasitoid model which is a non-dimensionalized Nicholson and Bailey model. Phase portraits are drawn for different ranges of parameters and display the complicated dynamics of this system. We conduct the bifurcation analysis with respect to intrinsic growth rate r and searching efficiency a. Many forms of complex dynamics such as chaos, periodic windows are observed. Transition route to chaos dynamics is established via period-doubling bifurcations. Conditions of occurrence of the period-doubling, Neimark-Sacker and saddle-node bifurcations are analyzed for b≠a where a,b are searching efficiency. We study stable and unstable manifolds for different equilibrium points and coexistence of different attractors for this non-dimensionalize system. Without the parasitoid, the host population follows the dynamics of the Ricker model.