Monitoring, Modeling, Dynamics, and Control of Leafhopper Pests in Tea Plantations

The tea green leafhopper Empoasca onukii is one kind of insect pests threatening the tea production. To reduce economic losses, pesticides are commonly used yet it causes the pest resistance, pest resurgence and the undesirable pesticide residues. Therefore, biological control has received increasing attention in recent years with the predatory mite Anystis baccarum as a potential agent. In this study, we aim to investigate the correlation and dynamics of E. onukii and A. baccarum and the mechanism for informing biological control.

Through the statistical modeling and analysis, we find intercropping treatments help to enhance the densities of the predatory mite, A. baccarum, and may reduce the populations of the leafhopper pest, E. onukii. Then, we analyze a predator-prey type of model with generalist predator and aim to understand the dynamics of E. onukii and A. baccarum for a purpose to develop a biological control strategy. We find that the nilpotent singularities are associated with a cubic Linard system, and the nilpotent bifurcations are three-parameter bifurcations of a codimension 4 nilpotent focus, and the degenerate nilpotent focus serves as an organizing center to connect all the codimension 3 bifurcations in the system. One interesting observation is that we show numerically the existence of three limit cycles in the system. Finally, we incorporate the stage structure into our generalist predator prey model to better explore the complex dynamics and to find the window of time to promote the use of A. baccarum to control E. onukii. The complex dynamics are also observed. Moreover, the hatching rate of E. onukii eggs is associated with the classification of the nilpotent singularity, which impacts the dynamics of the system significantly. Our results suggest that extending the incubation time of E. onukii eggs can be beneficial for pest control.

We present bifurcation diagrams and numerical simulations from numerical tools are presented to illustrate and support our findings. Furthermore, we also find that the higher codimension bifurcations involving nilpotent singularities in the system are associated to the well-known Hilberts 16th problem. The existence of three limit cycles and associated bifurcations supplies an interesting angle to understand the dynamics of planar systems when we consider them as a two-dimensional central manifold of the higher dimensional systems.