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 cont...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 perioddoubling bifurcation due to crop over-consumption by the pest population.We draw a Poincare 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.展开更多
基金Dibyendu Sekhar Mandal thankfully acknowledges the University Grants Commission(Rajiv Gandhi National Fellowship for SC/ST Candidates)of India(Grant/Award Number:F1-17.1/2013-14/RGNF-2013-14-SC-WES-53863/(SA-III/Website)for the financial assistance in the form of Senior Research FellowshipA.Chekroun and M.Helal are supported by the DGRSDT,Algeria.
文摘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 perioddoubling bifurcation due to crop over-consumption by the pest population.We draw a Poincare 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.
