Session S15 - Mathematics of Planet Earth

Tuesday, July 20, 17:30 ~ 17:55 UTC-3

The dynamics of predatory mite and the pest leafhopper with stage structure in a tea plantation

Huaiping Zhu

York University, Canada   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The tea green leafhopper \textit{Empoasca onukii} Matsuda (Hemiptera: Cicadellidae) is one of the most predominant insect pest threatening the tea production. Based on our earlier studies of the surveillance data, I will present pest control models in tea plantations where a generalist predator mite (Anystis baccarum) serves as a natural enemy to control green leafhopper Empoasca (E. onukii). These models contain life cycle of the pest leafhopper \textit{E. onukii} in three stages, including egg, nymph and adults. In this talk, I will presented bifurcations including saddle-node bifurcation of codimension 1 and 2, Hopf bifurcation, Bogdanov-Takens bifurcation, in particular, I will focus on the nilpotent singularities and their bifurcations. The existence of two or three limit cycles suggest that the tri-stability is possible. This study will help to develop the plausible control mechanism of \textit{E. onukii} by stages.

Joint work with Pei Yuan (York University) and Lilin Chen (Fujian Agriculture and Forestry University).

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