Bifurcation analysis and hormetic effects in a discrete-time plant
quality and larch budmoth interaction model
- Xiaohua Ren,
- Changcheng Xiang,
- Yi Yang
Changcheng Xiang
Hubei Minzu University
Corresponding Author:xcc7426681@126.com
Author ProfileAbstract
In recent years, the control of the larch budmoth has attracted a great
deal of attention from experts, and spraying with insecticides is one of
the main control strategies. The key of this strategy is the timing and
efficiency of insecticide applications and how multiple insecticide
applications affect the growth of budmoth. This paper extends a new two
dimensional discrete model by adding chemical controls based on a
dynamical model of plant quality interacting with larch budmoth proposed
in the literature to cope with this problem. First, the parametric
conditions required for the existence and local stability of the
positive fixed point of the model are discussed, and under certain
conditions, the presence of period-doubling bifurcation and
Neimark-Sacker bifurcation of the system, which reveals a significant
effect of the kill rates of insecticides on the budmoth growth. The
results show that a paradox arises when low kill rates stimulate the
growth of budmoth and high kill rates inhibit the growth of budmoth.
Furthermore, we analyze the influence of various factors and cumulative
effects on the paradox phenomenon. Therefore, the timing of insecticide
application and its efficiency should be chosen wisely to prevent the
paradox.