Dynamic Complexities in Competing Parasitoid Species on a Shared Host

In this study, we extend the two-dimensional host–parasitoid model to a one-host–two-parasitoid model, whose dynamic behaviors are more complex. As evidence, exploring the dynamic interaction between a host and its parasitoids provides significant insight into the biological control. Specifically, we demonstrate the existence of equilibrium points and explore their local stability properties, which are concerned with the effective biological control project. Furthermore, the transition between population fluctuations and the steady state is achieved via a bifurcation process, and we derive the occurrence conditions of the Neimark–Sacker bifurcation in the proposed system using an explicit criterion. To control population fluctuations and chaotic behaviors, two feedback control strategies are implemented in this system. Finally, the numerical simulations support our theoretical results and show the related biological phenomena.