一类具有Holling Ⅲ反应的害虫治理的Filippov模型研究
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摘要
在不采用任何害虫治理措施下给出了一个具有Holling Ⅲ反应的害虫及天敌模型,求出了该模型的平衡点,并讨论了平衡点的稳定性条件.为了把害虫的种群数量控制在经济临界值ET以内,建立了一个具有阈值控制策略的害虫治理Filippov模型,研究了该模型的动力学性质,包括模型的滑线区域,真、假平衡点及伪平衡点的存在性和稳定性.
The Filippov model is proposed in this paper that has a Holling Ⅲ reaction of pests and natural enemies. The equilibrium point of the model is figured out and the stability conditions of equilibrium point is discussed. In order to control the population quantity of pests within the economic threshold ET, the Filippov model of pest control with the threshold control strategy is established. Besides, the dynamic property of the model including the slip line model, the existence and stability of the true and false equilibrium points and pseudo-equilibrium point are systematically studied.
The Filippov model is proposed in this paper that has a Holling Ⅲ reaction of pests and natural enemies. The equilibrium point of the model is figured out and the stability conditions of equilibrium point is discussed. In order to control the population quantity of pests within the economic threshold ET, the Filippov model of pest control with the threshold control strategy is established. Besides, the dynamic property of the model including the slip line model, the existence and stability of the true and false equilibrium points and pseudo-equilibrium point are systematically studied.
引文
[1] Lu Z H, Chi X B, Chen L S. Impulsive control strategies in biological control of pesticide[J]. Theor Popul Biol, 2003,64(1):39-47.
[2] Liu B, Tian Y, Kang B L. Dynamics on a HollingⅡpredator-prey model with state-dependent impulsive control[J].Int J Biomath, 2012, 5(3):126006.
[3]TangSY,LiangJH,XiaoYN.SlidingbifurcationofFilippovtwostagepestcontrolmodelswitheconomic thresholds[J]. Soc Ind Appl Math, 2012, 72(4):1061-1080.
[4]丛继光,刘兵,康宝林.关于一类害虫治理流行病Filippov模型的动力学性质分析[J].生物数学学报,2013,28(4):617-622.
[5]尚晋,刘兵,康宝林.一个两阶段结构害虫治理Filippov模型的动力学性质研究[J].生物数学学报,2013,28(3):485-492.
[6]王爱丽.Filippov传染病模型在森林病虫害治理中的应用[J].河南科学,2014,32(7):1177-1180.
[7]王永存,刘兵,康宝林.一类具有HollingⅡ反应的害虫治理的Filippov模型的研究[J].生物数学学报,2015,30(1):63-68.
[8]韦创文,雒志学,杜明银.具有HollingⅡ类功能反应函数的食饵-捕食系统的定性分析[J].温州大学学报(自然科学版),2009,30(2):6-10.
[2] Liu B, Tian Y, Kang B L. Dynamics on a HollingⅡpredator-prey model with state-dependent impulsive control[J].Int J Biomath, 2012, 5(3):126006.
[3]TangSY,LiangJH,XiaoYN.SlidingbifurcationofFilippovtwostagepestcontrolmodelswitheconomic thresholds[J]. Soc Ind Appl Math, 2012, 72(4):1061-1080.
[4]丛继光,刘兵,康宝林.关于一类害虫治理流行病Filippov模型的动力学性质分析[J].生物数学学报,2013,28(4):617-622.
[5]尚晋,刘兵,康宝林.一个两阶段结构害虫治理Filippov模型的动力学性质研究[J].生物数学学报,2013,28(3):485-492.
[6]王爱丽.Filippov传染病模型在森林病虫害治理中的应用[J].河南科学,2014,32(7):1177-1180.
[7]王永存,刘兵,康宝林.一类具有HollingⅡ反应的害虫治理的Filippov模型的研究[J].生物数学学报,2015,30(1):63-68.
[8]韦创文,雒志学,杜明银.具有HollingⅡ类功能反应函数的食饵-捕食系统的定性分析[J].温州大学学报(自然科学版),2009,30(2):6-10.