一类具有非线性脉冲的捕食与被捕食系统的定性分析  

Analysis of the Predator-Prey Model With Nonlinear Impulsive Control

作　　者：李畅通[1,2] LI Changtong(School of Science,Xi’an Technological University,Xi’an 710021,P.R.China;School of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,P.R.China)

机构地区：[1]西安工业大学理学院,西安710021 [2]陕西师范大学数学与信息科学学院,西安710062

出　　处：《应用数学和力学》2020年第5期568-580,共13页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(61772017)。

摘　　要：实际的害虫控制策略由于受到资源有限、种群密度的影响,具有饱和效应或非线性特征.因此,该文对一类具有非线性脉冲控制策略的捕食与被捕食模型进行了全局定性分析.利用脉冲微分方程中的Floquet理论和比较方法,得到模型的天敌根除周期解全局渐近稳定的充分条件,通过分支理论,得到非平凡周期解存在性的条件,数值模拟验证了具有非线性脉冲的模型具有非常复杂的动态行为.Due to limited resources and population densities,the actual pest control strategies such as spraying pesticide and releasing natural enemies have saturation effects or nonlinearity.Therefore,a predator-prey model with nonlinear impulsive control due to resource limitation was proposed and analyzed.With the Floquet theory and the differential comparison principle,the condition for global stability of the predator-free periodic solution was provided.It is shown that once a threshold condition is met,a stable nontrivial periodic solution will emerge via a supercritical bifurcation.The numerical results show that the predator-prey model with nonlinear pulse has rich dynamical behaviors.

关 键 词：全局稳定 周期解 非线性脉冲 害虫控制 

分 类 号：Q241.8[生物学—细胞生物学] O242[理学—计算数学]