摘要
由于资源的有限性以及害虫群体对杀虫剂的抗性发展等因素,使得杀虫剂对害虫的杀死率具有饱和效应.因此,当害虫的数量达到经济阈值时,杀虫剂对害虫的杀死率与经济阈值有关.为了刻画上述饱和效应,建立了一类非线性脉冲状态依赖捕食被捕食模型.利用Lambert W函数和脉冲半动力系统的相关技巧,分析了模型阶1正周期解的存在性和稳定性,得到了相应的充分条件.进而讨论了非线性脉冲与线性脉冲对阶1周期解存在性的影响.
Due to the limited resources as well as the development of pests＇ resistance to pesti-cides, the instant killing rate of pesticide applications with respect to the pest could depend on the density of pest populations. Thus, the instant killing rate is a function of economic thresh-old （ET） once the density of pest population reaches the ET and integrated control tactics are implemented. In order to depict the saturation effects, a prey-predator model with nonlinear state-dependent impulsive effects was proposed. Using the Lambert W function and the analyti-cal techniques of the impulsive semi-dynanucal system, the sufficient conditions which guaran-teed the existence, local and global stability of order 1 positive periodic solution of the pro-posed model were obtained. Further, the effects of nonlinear impulse on the existence of order 1 periodic solution was discussed.
出处
《应用数学和力学》
CSCD
北大核心
2013年第5期496-505,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金资助项目(11171199)
