Complex Dynamics and Bifurcations in a Discrete Switching Host-Parasitoid Model under a Nonlinear Threshold Policy

In this study, we present a discrete switching host-parasitoid model that incorporates biological and chemical control interventions within the integrated pest management (IPM) measures. The coupling of multi-tactic control measures induces rich and complex dynamical behaviors in the proposed system. We begin by systematically characterizing the existence and stability of fixed points in the control subsystem. The analysis then proceeds to demonstrate how the system undergoes multiple bifurcation routes, including period-doubling, transcritical, and Neimark-Sacker bifurcations. Building on this theoretical foundation, extensive numerical simulations are conducted, not only corroborating our analytical predictions but also revealing emergent phenomena such as cascading period-doubling routes and chaotic regimes. Finally, high-resolution two-parameter stability diagrams are employed to identify the critical dynamical transition boundaries, and the corresponding ecological implications for practical pest management decision-making are elaborated in depth.