An Approach to Local Stability Analysis and Bifurcations of a Discrete-Time Host-Parasitoid Model

In this paper, we examine a discrete-time Host-Parasitoid model which is a non-dimensionalized
Nicholson and Bailey model. Populations have non-overlapping generations, discrete-time models will
be more rational and applicable than the continuous time models 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 perioddoubling,
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. The present work helped us to understand the
dynamical behavior of host-parasitoid interactions with intraspecific which can be used to improve the
classical biological control of parasitiods.