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1.
关于三种群第Ⅱ类功能性反应周期系数模型的研究   总被引:26,自引:5,他引:21  
本文讨论了一类三种群周期系数第Ⅱ类功能性反应模型,得到了其存在全局渐近稳定周期解及唯一性的条件.  相似文献   

2.
血吸虫是一种寄生在脊椎动物上有助于消化的地方或血管中的寄生虫.它们共有复杂的生活史,其中包括中间阶段的软体动物和一个脊椎动物宿主.根据MacDonald和May的工作,我们研究了一个基于血吸虫生活史的多个时滞的动力学模型,并且包含了一个由May和Wo11house提出的交配函数,当我们改变交配函数中的一个参数,血吸虫病的动力学行为从一个持久的疾病传播变成了疾病消失.如果增加雌性血吸虫的成熬周期,或交配周期和产卵周期,我们能够观察到长时间疾病传播的瞬时振动,这说明了对疾病的预测不依赖在一个特定时间的疾病水平,而是依赖一个充分长时间的疾病水平。  相似文献   

3.
离散广义LOGISTIC模型的渐进性态和混沌现象   总被引:1,自引:1,他引:0  
1引言自Li-Yorke的著名论文《3一周期意味混饨》问世以来,人们对一维离散模型进行了大量细致的研究工作,其中Logistic模型研究的最为彻底,并由此得到一系列普遍适用的理论结果[‘’2]文【3jIw接地对广义LOgistiC模型的稳定性及其吸引域进行了细致的研究,但其结论尚有不完善之处.在研究其周期解及混炖现象时,仅在IUI<1时对其近似模型进行了初步讨论·这里参数C>0为种群内禀生长率,U>一1表示种群对环境(包括营养资源等)利用率程度的参数.显然,当U—0时,模型(2)可化为LOgistiC模型(1).本文将直接对模型(2)进行…  相似文献   

4.
一类带时滞竞争模型的周期解   总被引:2,自引:0,他引:2  
研究了来源于水生种群植化相克的模型,提出了带时滞的半线性抛物系统.用上下解方法讨论了抛物方程组周期解存在性的原理,利用特征函数构造所提出抛物系统的上解,给出了正周期解存在的充分条件.  相似文献   

5.
讨论了一类具有阶段结构和第Ⅱ类功能反应的三种群混合模型,其中捕食种群具有阶段结构.得到在适当的条件下系统的持续生存,对应周期系统正周期解的存在性、唯一性以及全局稳定性.  相似文献   

6.
扩散与时滞有关的单种群植物模型的全局稳定性   总被引:1,自引:0,他引:1  
研究了具有周期系数及扩散与时滞有关的单种群植物模型,得到了该系统存在全局渐近稳定的正周期解的充分条件,其中该条件依赖时滞与扩散  相似文献   

7.
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   

8.
研究了一类疾病仅在食饵中传播的非自治捕食者-食饵模型.文中假定捕食者受密度制约影响,在捕食时具有甄别能力而只捕食健康的食饵,且具有HollingⅢ类功效函数;对于食饵,将其分为食饵易感者和食饵染病者两类,模型假定疾病发生率为非线性的,且考虑到了环境对食饵种群的容纳量.文中运用Barbalat引理、比较原理等稳定性理论的相关方法,找到了系统的正向不变集,证明了模型解的最终有界性;通过理论分析,分别得到了两种群持续生存、周期解的存在性以及周期解全局渐进稳定的相关条件;最后,通过MATLAB数值模拟,验证了有关结论.  相似文献   

9.
一类饲养业中发生的传染病模型的全局分析   总被引:1,自引:0,他引:1  
根据当所饲养的禽畜发生传染病时饲养业者的实际行为,研究了具有常数输入且输入者中必含潜伏期者的SEQ(I)S模型.利用三维竞争系统的Poincare-Bendixson性质排除了周期解的存在,证明了唯一的疾病存在平衡点的全局稳定性.  相似文献   

10.
应用重合度理论讨论了具有时滞的周期Schoener竞争模型,得到了系统正周期解存在的充分条件.  相似文献   

11.
We show the existence of a periodic solution in which four species coexist in competition for three essential resources in the standard model of resource competition. By assuming that species i is limited by resource i for each i near the positive equilibrium, and that the matrix of contents of resources in species is a combination of cyclic matrix and a symmetric matrix, we obtain an asymptotically stable periodic solution of three species on three resources via Hopf bifurcation. A simple bifurcation argument is then employed which allows us to add a fourth species. In principle, the argument can be continued to obtain a periodic solution adding one new species at a time so long as asymptotic stability can be assured at each step. Numerical simulations are provided to illustrate our analytical results. The results of this paper suggest that competition can generate coexistence of species in the form of periodic cycles, and that the number of coexisting species can exceed the number of resources in a constant and homogeneous environment.  相似文献   

12.
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   

13.
三种群食饵系统的平稳振荡   总被引:4,自引:1,他引:3  
本文研究了一类三种群周期食饵系统,并给出了其存在平稳振荡的充分条件。  相似文献   

14.
According to the economic and biological aspects of renewable resources management, we propose a Lotka–Volterra predator–prey model with state dependent impulsive harvest. By using the Poincaré map, some conditions for the existence and stability of positive periodic solution are obtained. Moreover, we show that there is no periodic solution with order larger than or equal to three under some conditions. Numerical results are carried out to illustrate the feasibility of our main results. The bifurcation diagrams of periodic solutions are obtained by using the numerical simulations, and it is shown that a chaotic solution is generated via a cascade of period-doubling bifurcations, which implies that the presence of pulses makes the dynamic behavior more complex.  相似文献   

15.
三种群非自治系统的周期解的吸引性   总被引:4,自引:0,他引:4  
本文讨论了三种群非自治竞争系统,此系统中所有的参数是与时间相关的,并且分别渐近接近于周期函数,得到了保证周期解吸引性的条件。  相似文献   

16.
高维非自治系统的周期解   总被引:1,自引:0,他引:1  
本文通过建立并利用齐次线性方程解的估计公式,获得了周期系统(1)的周期解的存在性、唯一性定理,对周期系统(2)给出了一个平稳振荡定理,最后给出了实例。  相似文献   

17.
An approximate, computationally tractable solution is proposed for the potentials in the bidomain model with periodic intracellular junctions (the periodic bidomain model). This new approach is based on the one-dimensional rigorous spectral method described previously by Trayanova and Pilkington (IEEE Trans. Biomed. Eng., May 1993). The total solution to the one-dimensional periodic bidomain problem is decomposed in the spectral domain into solutions to (1) the single-fiber classical bidomain problem in which the intracellular conductivity value incorporates the average contribution from cytoplasm and junction and (2) the “junctional” potential problem due to the presence of junctions at discrete locations alone. Solving for the junctional term rigorously requires most of the numerical effort in the solution for the periodic bidomain potentials. Here the junctional potential is found approximately with little numerical effort. A comparison between the rigorous and the approximate solutions serves as a justification for the proposed approximate solution procedure. The procedure outlined in this paper is applicable to higher spatial dimensions where both tissue anisotropy and junctional inhomogeneities play a role in establishing the transmembrane potential distribution.  相似文献   

18.
Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host’s intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.  相似文献   

19.
1IntroductionThesurvivalofspeciesisoneofthemostinterestingqllestionsinmathematicalbiology.Persistenceisanimportantconcepttodealwiththisproblem.Recently,manyauthorsfindthatthediffusionprocessinecologicalsystemplaysanimportantrole.Therearemanyliteraturestoinvestigatethedynamicswithdiffusionprocess,butfewerliteraturetoinvestigatethedynamicswithbothdiffusionprocessandfunctionalresponse.Inthispaper,theauthorswillbedevotetostudythethreespeciesdiffosiveprey-predatorsystemwithfunctionalresponseasfoll…  相似文献   

20.
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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