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Threshold strategy for nonsmooth Filippov stage-structured pest growth models. (English) Zbl 1435.92065

Summary: In order to control pests and eventually maintain the number of pests below the economic threshold, in this paper, based on the nonsmooth dynamical system, a two-stage-structured pest control Filippov model is proposed. We take the total number of juvenile and adult pest population as the control index to determine whether or not to implement chemical control strategies. The sliding-mode domain and conditions for the existence of regular and virtual equilibria, pseudoequilibrium, boundary equilibria, and tangent points are given. Further, the sufficient condition of the locally asymptotic stability of pseudoequilibrium is obtained. By numerical simulations, the local bifurcations of the equilibria are discussed. Our results show that the total number of pest populations can be successfully controlled below the economic threshold by taking suitable threshold policy.

MSC:

92D25 Population dynamics (general)
34A36 Discontinuous ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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