Local Dynamics of a Discrete-time Host-Parasitoid Model

In this chapter,We investigate a non-dimensionalized Nicholson and Bailey discrete-time Host-Parasitoid model. For various parameter ranges, phase portraits are made to show the system's complex dynamics. With regard to intrinsic growth rate r and searching efficiency a, we perform the bifurcation analysis. We see a wide variety of complex dynamics, including chaos and periodic windows. Period- doubling bifurcations are used to build a path to chaotic dynamics. Conditions of occurrence of the period-doubling, Neimark-Sacker and saddle-node bifurcations are analyzed for b a where a, b are searching efficiency. At this non-dimensionalize system, we investigate stable and unstable manifolds for various equilibrium points as well as the presence of various attractors. The host population behaves according to the Ricker model's dynamics in the absence of the parasitoid. We were able to better comprehend the dynamical behaviour of host-parasitoid interactions with intraspecific knowledge from the current work, which can be employed to enhance the traditional biological management of parasitoids.