Dynamic Behaviors and Bifurcation Analysis of a Three-Dimensional Filippov Ecosystem With Fear Effect

Abstract

A Filippov system of crop-pest-natural enemy with a Holling-II type functional response function is developed based on the fear effect and threshold control strategy. The threshold control strategy is mainly a means of controlling pests and natural enemies. When the number of natural enemies is below a threshold, the natural enemies cannot achieve a controlling effect on the pest population and control is needed to suppress the outbreak. In this case, the fear of pests to natural enemies will affect the pest's survival mode, thus affecting the pest's dynamic behavior. However, the number of natural enemy population exceeds the threshold density, and there is no need to control the system. At this point, the pest's fear of natural enemies is almost zero. The dynamic behavior of the two subsystems of the model is discussed, the existence and stability of various equilibria are analyzed, and the existence of sliding and crossing regions is also investigated. In addition, it is possible that the established model has more than one pseudo-equilibrium. Therefore, the dynamic behavior of the pseudo-equilibria is analyzed, and we observe that Hopf bifurcation occurs near the pseudo-equilibria. By numerically simulating the global sliding bifurcation of the system, we discover that as the bifurcation parameters are varied, the system exhibits a series of bifurcations such as grazing bifurcation, buckling bifurcation, crossing bifurcation, and period-halving bifurcation.