n种群Lotka-Volterra周期系数捕食-竞争系统周期解的存在性与全局吸引性

在本文中,作者考察了n种群Lotak-Volterra周期捕食-竟争系统,用比较定理、Brouwer不定点定理和V函数方法证明了正解的最终有界性、正周期解的存在性、正周期解的全局吸引性及唯一性．     

Harvesting on a stage-structured single population model with mature individuals in a polluted environment and pulse input of environmental toxin

In the natural world, there are many species whose individual members have a life history that they take them with two distinct stages: immaturity and maturity. In particular, we have in mind mammalian populations and some amphibious animals. We improve the assumption of a single population as a whole. It is assumed that the immature individuals and mature individuals are divided by a fixed period. This paper concentrates on the study of a stage-structured single population model with mature individuals in a polluted environment and pulse input of environmental toxin at fixed moments. Furthermore, the mature individuals are harvested continuously. We show that the population goes extinct if the harvesting rate is beyond a critical threshold. Conditions for the extended permanence of the population are also examined. From the biological point of view, it is easy to protect species by controlling the harvesting amount, impulsive period of the exogenous input of toxin and toxin impulsive input amount, etc. Our results provide reasonable tactics for biological resource management.     

Periodic Solutions of N-Species Competition System with Time Delays

1IntroductionWeconsiderherethefollowingpeiodicn-speCiescompetitionSyStemwithtimedelaystogetherwithinitialvalueconditionswherer,(i=1,..',n)arepeitivecontinuousdeperiedicfUnctionsandail,ry(i,j=1,...f,n)arenormeqativeconStants.Whenr.(i=1,..',n)arepeitiveconStants,(1.1)isknoWnasan"speCies~a-VolterracompetitionsystemintheliteratureonmathematicaleCOIOgyandhashostudiedextensivelybySevelal.thorstl-j.ShibataandAntot')haveshownthetimedelaysinatwcrspeCies~a-Volterra~itionsystemcanleadto"~ic~ior".O…     

具有时滞的非自治差分竞争系统的持久生存性和全局稳定性(英文)

对一类具有时滞的两种群竞争系统进行了研究,利用一些不等式的技巧得到了系统持久生存的充分条件,并且通过构造一个离散的Lyapunov函数得到了系统正解全局稳定的条件.     

具收获与脉冲的时滞捕食模型研究

研究了与生物资源管理相关的食饵具脉冲扰动与成年捕食者具连续收获的阶段结构时滞捕食-食饵模型.利用离散动力系统的频闪映射和脉冲时滞微分方程理论,得到了捕食者灭绝周期解的全局吸引和系统持久的充分条件,也证明了系统的所有解的一致完全有界.结论为现实的可再生生物资源管理提供了可靠的策略依据.     

带有干扰和非线性指标的脉冲时滞SI模型的渐近性质(英文)

研究了一个带有干扰和非线性指标的脉冲时滞SI模型,通过引入三个引理,获得该疾病最终灭绝和保持持久的充分性条件。结果表明,时滞因素对该模型的全局吸引性和持久性都有影响。此外。如果脉冲免疫接种率的最大值和最小值之比大于某一阈值,则该疾病最终灭绝,本文的主要特点是将多时滞和变系数引入脉冲SI模型,数值模拟表明,该系统具有复杂的动力学行为,包括周期解和周期振荡.     

具有时滞的非自治差分竞争系统的渐近行为研究(英文)

提出了一个具有时滞的非自治差分竞争系统.分别利用差分不等式及Lyapunov离散函数技巧,得到了系统永久持续生存和正解全局吸引的充分条件.数值模拟验证了理论结果的正确性.     

一类具有阶段结构和脉冲效应的捕食者-食饵模型的动力学分析

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.     

Impulsive Vaccination of an SEIRS Model with Time Delay and Varying Total Population Size

Pulse vaccination is an effective and important strategy for the elimination of infectious diseases. A delayed SEIRS epidemic model with pulse vaccination and varying total population size is proposed in this paper. We point out, if R* < 1, the infectious population disappear so the disease dies out, while if R _*; > 1, the infectious population persist. Our results indicate that a long period of pulsing or a small pulse vaccination rate is sufficient condition for the permanence of the model.     

具脉冲扩散效应的单种群动力学模型

讨论了两斑块间脉冲扩散的单种群动力学模型,利用离散动力系统频闪映射理论,得到了种群持续生存的充分条件．结论31,1~了现实的生物种群动力学性质,也丰富了脉冲微分方程理论．     

Permanence and global attractivity for Lotka–Volterra difference systems

 The permanence and global attractivity for two-species difference systems of Lotka–Volterra type are considered. It is proved that a cooperative system cannot be permanent. For a permanent competitive system, the explicit expression of the permanent set E is obtained and sufficient conditions are given to guarantee the global attractivity of the positive equilibrium of the system. Received: 21 May 1997 / Revised version: 25 November 1998     

一个造血模型的概周期正解的存在唯一性和全局吸引性

本文讨论了一类具有无穷时滞的泛函微分方程 N′（t）=-α（t）N（t）＋b（t）∫0^∞K（s）e^-q（t）N（t-s）ds,t≥0, 正概周期解的存在唯一性和全局吸引性问题,利用锥中不动点定理,不仅得到了上述系统的正概周期解的存在唯一性和全局吸引性的结论,还改进了文献[15]的主要结果,并且我们的方法比压缩映象原理要好．如果（＊）中所有的系数都为周期的,相应的结论也是成立的,此时,我们的结果也推广了现有文献的结论．     

具性别和阶段结构的非自治二种群捕食者-食饵系统研究

讨论了一类食饵具有性别结构,捕食者具有阶段结构的非自治捕食者．食饵系统,运用Liapunov函数方法,得到了该系统一致持续生存的充分条件．对于该模型的周期系统,在适当条件下,存在唯一、全局渐近稳定的周期解．对更具普遍意义的概周期现象,也得出了概周期正解唯一存在且全局渐近稳定的充分条件．     

一类食饵具有S-型变收获率的非自治离散捕食系统渐近行为

建立并研究了一类具有S-型变收获率的非自治离散捕食系统,应用差分不等式、Brouwer不动点定理和分析技巧分别建立了系统的持久生存性,正周期解的存在性及全局渐近稳定性的充分条件,我们还给出了具体验证例子及相应的数值模拟结果.     

非自治阶段结构与时滞捕食模型的持久性和周期解

讨论了一类非自治阶段结构带有消化时滞的两种群捕食模型,其中只有一个种群有阶段结构,本文得到了这个系统能够持久生存的条件．进一步,如果这个系统是周期系统我们证明了在一定条件下系统存在唯一的全局渐近稳定的正周期解。     

变系数变时滞BAM神经网络概周期解的存在性与全局吸引性

利用指数二分性、Banach不动点定理与微分不等式分析技巧,在不要求激活函数有界的条件下,给出了变系数变时滞的BAM神经网络概周期解的存在唯一性和全局吸引性的充分条件．所得结果推广和改进了相应文献的结果。对设计BAM神经网络概周期振荡有重要意义．     

Persistence in periodic and almost periodic Lotka-Volterra systems

It is shown that a strongly self-regulating (or resource limited) Lotka-Volterra population system can persist in a periodic or almost periodic environment if and only if the system tracks the environmental variations.     

Convergence in almost periodic Fisher and Kolmogorov models

 We study convergence of positive solutions for almost periodic reaction diffusion equations of Fisher or Kolmogorov type. It is proved that under suitable conditions every positive solution is asymptotically almost periodic. Moreover, all positive almost periodic solutions are harmonic and uniformly stable, and if one of them is spatially homogeneous, then so are others. The existence of an almost periodic global attractor is also discussed. Received: 11 November 1996 / Revised version: 8 January 1998