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具有扩散和时滞的捕食系统的持续生存 总被引:3,自引:0,他引:3
本文研究具有一般功能性反应和时滞的周期捕食系统的持续生存和周期解,得到了系统永久持续生存的充要条件.在此条件下系统存在正的ω周期解,改进了一些已知结果. 相似文献
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研究了有m个捕食者n个食饵的概周期Lotka-Volterra系统.得到了系统共存的条件.此外,还得到了系统概周期解存在唯一并且全局渐近稳定的条件. 相似文献
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具有脉冲效应和综合害虫控制的捕食系统 总被引:8,自引:1,他引:7
本文通过生物控制和化学控制提出了具有周期脉冲效应与害虫控制的捕食系统. 系统保护天敌避免灭绝,在一些条件下可以使害虫灭绝.就是说当脉冲周期小于某一临界值时,存在全局稳定害虫灭绝周期解.脉冲周期增大大于临界值时,平凡害虫灭绝周期解失去稳定性并产生正周期解,利用分支理论来研究正周期解的存在性.进而,利用李雅普诺夫函数和比较定理确定了持续生存的条件. 相似文献
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研究了一类具第三类功能反应且食饵具有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下,系统存在全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件. 相似文献
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讨论一类包含一组线性时变子系统和一个周期切换信号的切换系统的稳定性.在系统满足一定条件的情况下,利用Floquet定理,给出了周期线性时变切换系统指数稳定的充分必要条件. 相似文献
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研究了捕食者具有阶段结构且食饵有避难所的非自治捕食系统.利用Lyapunov函数方法得到了系统持续生存的条件,以及在一定条件下存在唯一全局渐进稳定的周期正解.对于更广泛的概周期现象,也得到了存在唯一全局渐进稳定的概周期正解的充分条件. 相似文献
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具有Holling Ⅱ类功能反应且周期系数的非自治捕食扩散系统的持久与全局渐近稳定性 总被引:7,自引:0,他引:7
研究了一类具有扩散系数和 Holling 类功能反应的一捕两食三种群非自治捕食系统 ,得到了系统持久生存和周期系统存在唯一全局渐近稳定的周期解的条件 . 相似文献
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赵文才 《数学的实践与认识》2009,39(17)
建立了一类具有隔离和垂直传染的SIQR传染病模型,在脉冲免疫接种条件下,分析了其全局动力学行为.利用频闪映射,获得了无病周期解,给出了此周期解的全局稳定性分析.并获得了系统一致持续生存的条件. 相似文献
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Li YongKun 《系统科学与数学》2000,13(1)
In this paper, we establish the existence of a positive periodic solution for a periodic delay single species population growth model, and obtain sufficient conditions for the periodic solution to be globally attractive. 相似文献
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1IntroductionTl1eage-structuredpopulationmodelhasbeensuccessfullyusedinpopulationdynamics['f'].Tl1egeneralage-structuredpopuIationmodelisdescribedbythefollowingpartialdifferentialequatiolls{3]:whereu(a,f)istheage-specificdensityofasingleage-structuredspeciesattimet,p(a,f)andb(a,t)aretheage-specificpercapitaldeathrateandbirthrateofthespeciesattimet,respectively.TherealAisthemaxinlulllageforanyindividuali11thepopulation,and[A1,A2listhefecundityperiodoffelllales.Thefunctiolluo(a)istheinitialdel… 相似文献
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In this paper, a HTLV-I infection model with CTL immune response is considered. Taking the immune delay as a bifurcation parameter we investigate the global existence of periodic solutions of this model which shows existence of multiple periodic solutions theoretically. 相似文献
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一个周期中立型对数种群模型 总被引:7,自引:0,他引:7
本文获得了周期中立型对数种群模型N(t)=N(t)(r(t)-α(t)log[N(t-σ)]-b(t)d/dtlog[N(t-r)])的周期正解的存在性及对所有正解的吸引性. 相似文献
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具饱和传染率的脉冲免疫接种SIRS模型 总被引:1,自引:0,他引:1
研究了具饱和传染率的脉冲免疫接种SIRS模型的一致持续生存和周期解,得到了无病周期解全局渐近稳定的充分条件和系统一致持续生存的充分条件,并应用分支理论得到了正周期解存在的分支参数. 相似文献
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蛙卵有丝分裂模型的定性分析 总被引:3,自引:2,他引:1
本文对M.T.Borisuk和J.J.Tyson在[1]中所提出的一个有关蛙卵有丝分裂的平面三次系统模型证明了大范围周期解的存在性,给出了周期解所在的空间区域和所对应的参数区域及周期解不存在的空间区域和参数区域,所得结果严格地证明了[1]中给出的数值结果,最后我们证明在[1]的数值结果所用的参数下极限环的唯一性。 相似文献
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We introduce a model of the growth of a single microorganism in a self-cycling fermentor in which an arbitrary number of resources are limiting, and impulses are triggered when the concentration of one specific substrate reaches a predetermined level. The model is in the form of a system of impulsive differential equations. We consider the operation of the reactor to be successful if it cycles indefinitely without human intervention and derive conditions for this to occur. In this case, the system of impulsive differential equations has a periodic solution. We show that success is equivalent to the convergence of solutions to this periodic solution. We provide conditions that ensure that a periodic solution exists. When it exists, it is unique and attracting. However, we also show that whether a solution converges to this periodic solution, and hence whether the model predicts that the reactor operates successfully, is initial condition dependent. The analysis is illustrated with numerical examples. 相似文献
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《Annals of Differential Equations》2012,(2):234-241
The positive periodic solutions to a three-species delayed Lotka-Volterra model with dispersion and harvesting terms are studied in this paper. By the coincidence degree theory, the sufficient conditions for existence of eight positive periodic solutions to the model are obtained. 相似文献
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Periodic solutions of a nonautonomous periodic model of population with continuous and discrete time
《Journal of Computational and Applied Mathematics》2006,188(2):256-264
In this paper, we employ the Mawhin's continuation theorem to study the existence of positive periodic solutions of the nonautonomous periodic model of population with continuous and discrete time. It is interesting that the conditions to guarantee the existence of positive periodic solutions of discrete time model are similar to those for the corresponding continuous time model. 相似文献