共查询到19条相似文献,搜索用时 125 毫秒
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文章讨论一类捕食者(天敌)具脉冲放养与食饵(害虫)具阶段结构时滞的捕食-食饵模型,得到了害虫灭绝周期解全局吸引的充分条件和害虫的密度可以控制在经济危害水平E(EIL)之下的脉冲存放周期.为现实的害虫管理提供一定的理论依据. 相似文献
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研究了具有脉冲作用和功能反应的二阶食饵一捕食系统.利用脉冲微分方程的F1quet乘子理论、比较定理等方法,证明了当脉冲周期小于某个临界值时,系统存在一个全局渐进稳定的害虫灭绝周期解,并说明了系统的解是一致最终有界的. 相似文献
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研究了一类食饵受病毒感染的生态流行病模型,考虑脉冲释放病毒颗粒和自然天敌来进行害虫治理.利用Floquet乘子理论、小振幅扰动技巧和比较定理证明了害虫灭绝周期解的全局渐近稳定性以及系统持续生存的充分条件.结果为现实的害虫管理提供了科学依据. 相似文献
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研究了一个捕食者具有阶段结构,食饵具有脉冲效应和时滞的捕食者-食饵模型.利用离散动力系统的频闪映射,我们获得了捕食者-灭绝的周期解同时给出了该周期解全局吸引的充分条件.利用时滞脉冲微分方程的理论,得到了系统持续生存的充分条件. 相似文献
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建立并研究了一类具有周期强迫和脉冲扰动的捕食模型,通过理论分析和数值模拟,得到了食饵灭绝周期解全局渐近稳定和系统持久的充分条件,利用分支理论证明了边界周期解附近会分支出正周期解. 相似文献
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研究了一个具有脉冲出生的Leslie-Gower捕食者一食饵系统的动力学性质.利用频闪映射。得到了带有Ricker和Beverton-Holt函数的脉冲系统准确的周期解.通过Floquet定理和脉冲比较定理,讨论了该系统的灭绝和持久生存.最后,数值分析了以b(p)为分支参数的分支图,得到的结论是脉冲出生会带给系统倍周期分支、混沌以及在混沌带中出现周期窗口等复杂的动力学行为. 相似文献
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Integrated pest management models and their dynamical behaviour 总被引:7,自引:0,他引:7
Two impulsive models of integrated pest management (IPM) strategies are proposed, one with fixed intervention times and the
other with these unfixed. The first model allows natural enemies to survive but under some conditions may lead to extinction
of the pest. We use a simple prey-dependent consumption model with fixed impulsive effects and show that there exists a globally
stable pesteradication periodic solution when the impulsive period is less than certain critical values. The effects of pest
resistance to pesticides are also studied. The second model is constructed in the light of IPM practice such that when the
pest population reaches the economic injury level (EIL), a combination of biological, cultural, and chemical tactics that
reduce pests to tolerable levels is invoked. Using analytical methods, we show that there exists an orbitally asymptotically
stable periodic solution with a maximum value no larger than the given Economic Threshold (ET). The complete expression for
this periodic solution is given and the ET is evaluated for given parameters.We also show that in some cases control costs
can be reduced by replacing IPM interventions at unfixed times with periodic interventions. Further, we show that small perturbations
of the system do not affect the existence and stability of the periodic solution. Thus, we provide the first demonstration
using mathematical models that an IPM strategy is more effective than classical control methods. 相似文献
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Plant disease mathematical models including continuous cultural control strategy and impulsive cultural control strategy are proposed and investigated. This novel theoretical framework could result in an objective criterion on how to control plant disease transmission by replanting of healthy plants and removal of infected plants. Firstly, continuous replanting of healthy plants and removing of infected plants is taken. The existence and stability of disease-free equilibrium and positive equilibrium are studied and continuous cultural control strategy is given. Secondly, plant disease model with impulsive replanting of healthy plants and removing of infected plants is also considered. Using Floquet's theorem and small amplitude perturbation, the sufficient conditions under which the infected plant free periodic solution is locally stable are obtained. Moreover, permanence of the system is investigated. Under certain parameter spaces, it is shown that a nontrivial periodic solution emerges via a supercritical bifurcation. Finally, our findings are confirmed by means of numerical simulations. The modeling methods and analytical analysis presented can serve as an integrating measure to identify and design appropriate plant disease control strategies. 相似文献
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讨论了一类在两个不同固定时刻分别释放染病害虫和喷洒农药且具有HollingⅡ类传染率的SI模型.通过脉冲微分方程的Floquet理论和小幅扰动技巧,证明了当释放的染病害虫数量超过某个临界值时,系统存在一个渐进稳定的易感害虫根除周期解,否则系统是持续生存的.通过数值模拟,验证了所得结论的正确性及系统动力学行为的复杂性,分析说明了所提出的脉冲控制策略的有效性. 相似文献
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Using successor functions and Poincaré-Bendixson theorem of impulsive differential equations, the existence of periodical solutions to a predator-prey model with two state impulses is investigated. By stability theorem of periodic solution to impulsive differential equations, the stability conditions of periodic solutions to the system are given. Some simulations are exerted to prove the results. 相似文献
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State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences 总被引:4,自引:0,他引:4
A state-dependent impulsive model is proposed for integrated pest management (IPM). IPM involves combining biological, mechanical, and chemical tactics to reduce pest numbers to tolerable levels after a pest population has reached its economic threshold (ET). The complete expression of an orbitally asymptotically stable periodic solution to the model with a maximum value no larger than the given ET is presented, the existence of which implies that pests can be controlled at or below their ET levels. We also prove that there is no periodic solution with order larger than or equal to three, except for one special case, by using the properties of the LambertW function and Poincare map. Moreover, we show that the existence of an order two periodic solution implies the existence of an order one periodic solution. Various positive invariant sets and attractors of this impulsive semi-dynamical system are described and discussed. In particular, several horseshoe-like attractors, whose interiors can simultaneously contain stable order 1 periodic solutions and order 2 periodic solutions, are found and the interior structure of the horseshoe-like attractors is discussed. Finally, the largest invariant set and the sufficient conditions which guarantee the global orbital and asymptotic stability of the order 1 periodic solution in the meaningful domain for the system are given using the Lyapunov function. Our results show that, in theory, a pest can be controlled such that its population size is no larger than its ET by applying effects impulsively once, twice, or at most, a finite number of times, or according to a periodic regime. Moreover, our theoretical work suggests how IPM strategies could be used to alter the levels of the ET in the farmers' favour. 相似文献
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Extinction and permanence of one-prey multi-predators of Holling type II function response system with impulsive biological control 总被引:3,自引:0,他引:3
In this paper, one investigates the dynamic behaviors of one-prey multi-predator model with Holling type II functional response by introducing impulsive biological control strategy (periodic releasing natural enemies at different fixed time). By using Floquet theorem and small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value and permanence condition is established via the method of comparison involving multiple Liapunov functions. It is shown that multi-predator impulsive control strategy is more effective than the classical and single one. 相似文献