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Sliding bifurcations of Filippov two stage pest control models with economic thresholds. (English) Zbl 1256.34038
Summary: In order to control pests, a specific management strategy called the threshold policy is proposed, which can be described by Filippov systems (or piecewise smooth systems). The aim of this work is to investigate a variety of bifurcation phenomena of equilibria and sliding cycles of Filippov two-stage structured population models with density dependent per capita birth rates and transition rates from the juvenile class into the adult class. It is shown that interadult competition alone can give rise to multiple sliding segments and multiple pseudoequilibria, whilst interadult and interjuvenile competition together can result in rich sliding bifurcations. As the threshold value varies, local sliding bifurcations including boundary node (saddle), tangency and pseudo-saddle-node bifurcations occur sequentially, and global sliding bifurcations including buckling bifurcations of the sliding cycles, sliding crossing bifurcations, and pseudohomoclinic bifurcations can be present. Threshold policy control has been shown to be easily implemented and useful in pest management, which can be used to prevent the possibility of multiple pest outbreaks or cause the density of pests to stabilize at a desired level such as an economic threshold.
MSC:
34C60Qualitative investigation and simulation of models (ODE)
34A36Discontinuous equations
92D25Population dynamics (general)
34C23Bifurcation (ODE)
34A37Differential equations with impulses
34C25Periodic solutions of ODE
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