Dynamic analysis of a delayed pest-natural enemy model: triple effects of non-monotonic functional response, additional food supply and habitat complexity

Considering the food diversity of natural enemy species and the habitat complexity of prey populations, a pest-natural enemy model with non-monotonic functional response is proposed for biological management of Bemisia tabaci. The dynamic characteristics of the proposed model are analyzed. In addition, considering that the conversion from prey to predator has a certain time lag rather than instantaneous, a time delay is introduced into this model, and it is shown that the Hopf bifurcation occurs at the interior equilibrium when the time delay is used as the bifurcation parameter. Furthermore, the values of the parameters that determine the direction of the Hopf bifurcation as well as the stability of the periodic solution are calculated. In order to illustrate the theoretical analysis results, numerical simulations and validation are carried out to demonstrate the effects of non-monotonic functional response, additional food supply and habitat complexity.