Study of a crop-pest-natural enemy model with Z-type control — An approach to pest management

Abstract

In this study, the Z-type control method is applied to an intraguild crop-pest-natural enemy model, assuming that the natural enemy can predate on both crop and pest populations. For this purpose, the indirect Z-type controller is considered in the natural enemy population. After providing the design function for the crop-pest-natural enemy model with Z-control, we find the analytical expression of the update parameter. The findings indicate that the uncontrolled system can produce chaos through period-doubling bifurcation due to crop over-consumption by the pest population. We draw a Poincaré map to confirm the occurrence of chaos and compute the maximum Lyapunov exponent. As the observations further indicate that the pest population can be controlled by using an indirect Z-control mechanism in the natural enemy population, we postulate that, if natural enemy abundance can be governed by the update parameter, any desired pest population abundance can be achieved through the proposed Z-type controller, thus controlling the pest. To verify these assertions, extensive numerical simulations are performed to explore the potential for practical application of the proposed Z-type controller.