Threshold control strategy for a non-smooth Filippov ecosystem with group defense

Abstract

A non-smooth Filippov ecosystem with group defense is proposed to investigate the effects of threshold and intermittent control strategy for IPM. The proposed model has been analyzed theoretically using the qualitative analysis techniques related to Filippov non-smooth systems in the first place. In particular, the existence and stability of equilibria are discussed for the sliding mode dynamics, through which it can be shown that the real equilibrium and pseudo-equilibrium can coexist. After that, some relevant topics such as sliding mode bifurcation, boundary-focus bifurcation, grazing bifurcation, crossing bifurcation and buckling bifurcation are investigated using numerical analysis. These complex sliding bifurcations reveal that the proposed Filippov system admits the coexistence of multi-attractors including equilibrium and crossing cycles, thus indicating that there exists a close relationship between the intermittent control strategy and the initial densities of both populations. Similarly, the global stability properties of real equilibrium and pseudo-equilibrium of subsystems show that the intermittent control strategy can effectively control the pests under the prescribed threshold which is the aim of the IPM strategy.