具有脉冲效应的害虫传染病防治模型的动力学行为
|
摘要
基于害虫综合治理策略,建立了具有Monod-Haldance功能性反应的不同固定时刻分别投放染病害虫、天敌和喷洒化学农药的传染病模型.通过脉冲微分方程的小振动技巧、Floquet定理和比较定理,得到传染病模型中易感害虫灭绝周期解渐近稳定(局部和全局)的条件.并且利用Matlab软件通过调节相应的参数进行验证,得到模型的正确性.同时接下来可以继续深入研究的方向和课题.此模型的适用性很强,在农林业中可以用来指导实践.
In the paper, we establish the pest-epidemic model with the Monod-Haldance functional response to present the process of periodic spraying pesticide and releasing natural enemies and infected insect at different fixed moments. The sufficient conditions for the local stability and the globally stability of prey eradication periodic solution are obtained by using the Comparison theorem and Floquet theorem. Finally, we use numerical simulations to verify the feasibility of the obtained results by Matlab. At the same time, the problems that can be further studied in this paper are given. This model has strong applicability, which can be used to guide practices.
In the paper, we establish the pest-epidemic model with the Monod-Haldance functional response to present the process of periodic spraying pesticide and releasing natural enemies and infected insect at different fixed moments. The sufficient conditions for the local stability and the globally stability of prey eradication periodic solution are obtained by using the Comparison theorem and Floquet theorem. Finally, we use numerical simulations to verify the feasibility of the obtained results by Matlab. At the same time, the problems that can be further studied in this paper are given. This model has strong applicability, which can be used to guide practices.
引文
[1] Christopher M. Heggerud, Kunquan Lan. Local stability analysis of ratio-dependent predator-prey models with predator harvesting rates[J]. Applied Mathematics and Computation, 2015, 270:349-357.
[2] Seunghyeon Baek, Wonlyul Ko, Inkyung Ahn. Coexistence of a one-prey two-predators model with ratio-dependent functional responses[J]. Applied Mathematics and Computation, 2017, 219(4):1897-1908.
[3]刘娟.具有状态脉冲效应的害虫防治模型[J].山西农业大学学报(自然版),2017, 37(3):173-176.
[4]刘娟,赵清,程彩萍等.具有脉冲效应的2个食饵1个捕食者系统的稳定性[J].江苏农业科学,2018,46(18):94-97.
[5]许玲.污染环境下一类害虫治理模型的数学研究[D].辽宁师范大学硕士论文,2011.
[6]周玉梅,焦建军.具密度依赖脉冲出生阶段结构单种群动力学模型研究[J].统计与决策,2012(16):20-21.
[7]官金兰,房少梅.具有时滞和HollingⅢ型功能反应的三种群捕食模型的全局渐近稳定性[J].韶关学院学报,2014, 35(4):5-9.
[8]胡杰,刘娟.具有比率功能性反应的脉冲鼠害防治系统[J].山西农业大学学报(自然版),2018, 38(9):37-42.
[9]康爱花,薛亚奎.疾病在食饵中流行的捕食与被捕食模型的分析[J].数学的实践与认识,2007, 37(10):77-81.
[10]宋新宇,郭红建,师向云.脉冲微分方程理论及其应用[M].北京:科学出版社,2011:165-197.
[2] Seunghyeon Baek, Wonlyul Ko, Inkyung Ahn. Coexistence of a one-prey two-predators model with ratio-dependent functional responses[J]. Applied Mathematics and Computation, 2017, 219(4):1897-1908.
[3]刘娟.具有状态脉冲效应的害虫防治模型[J].山西农业大学学报(自然版),2017, 37(3):173-176.
[4]刘娟,赵清,程彩萍等.具有脉冲效应的2个食饵1个捕食者系统的稳定性[J].江苏农业科学,2018,46(18):94-97.
[5]许玲.污染环境下一类害虫治理模型的数学研究[D].辽宁师范大学硕士论文,2011.
[6]周玉梅,焦建军.具密度依赖脉冲出生阶段结构单种群动力学模型研究[J].统计与决策,2012(16):20-21.
[7]官金兰,房少梅.具有时滞和HollingⅢ型功能反应的三种群捕食模型的全局渐近稳定性[J].韶关学院学报,2014, 35(4):5-9.
[8]胡杰,刘娟.具有比率功能性反应的脉冲鼠害防治系统[J].山西农业大学学报(自然版),2018, 38(9):37-42.
[9]康爱花,薛亚奎.疾病在食饵中流行的捕食与被捕食模型的分析[J].数学的实践与认识,2007, 37(10):77-81.
[10]宋新宇,郭红建,师向云.脉冲微分方程理论及其应用[M].北京:科学出版社,2011:165-197.