A study on pest control models based on nonlinear threshold control

Abstract

The pest number trigger threshold strategy has been widely used in the control of pests in agricultural production. In this study, pest populations are managed by using an integrated nonlinear threshold function and a saturation function. The existence conditions of various equilibrium points and sliding sections in the system are derived. Theoretical analysis and numerical simulation results show the existence of boundary equilibrium bifurcations, tangency bifurcations and limit cycle bifurcations caused by discontinuous boundary. It is worth noting that persistence and non-smooth folding can be observed in the boundary equilibrium bifurcations. At the same time, because the nonlinear threshold control strategy is adopted in this study, the change of the sliding section of the model is more complicated. The numerical simulation results show that if there is an unstable focus in the model, a sliding homoclinic cycle will appear with the occurrence of boundary saddle point bifurcation, and then form a crossing limit cycle. The sensitivity analysis results of the system show that if the threshold level is too low, the control measures do not achieve the desired results. Too high threshold selection will cause unnecessary economic losses. Therefore, our results show that an appropriate threshold should be set to reduce economic losses while ensuring that the number of pests is in a lower stable state.