Dynamic Complexity of a Nicholson-Bailey Bioeconomic Model with Holling Type-II Functional Response

In this paper, we propose a host-parasitoid model with a Holling type-II functional response and incorporate harvest effort. The Holling type-II response leads to saturation in parasitized hosts, creating a potential economic harvesting opportunity. To address overexploitation risks, we integrate a harvest effort function, determining an optimal threshold to prevent depletion. We explore model dynamics and bifurcations, including co-dimension one behaviors such as flip and Neimark-Sacker bifurcations, we provide numerical examples for validation. Our suggested difference-algebraic model, compared to continuous-time models, exhibits rich dynamics within the Nicholson-Bailey host-parasitoid framework.