关于一类污染治理的单种群模型的数学研究

以脉冲微分方程为基础,建立了一类污染环境中在固定时刻对污染进行治理的具有时滞效应的单种群阶段结构模型.详细研究了该模型的动力学性质,给出了种群灭绝和持续生存的充分条件,并进一步研究了污染治理和时滞效应对种群灭绝的影响.本文具有很强的生物意义,为环境污染治理问题提供了可靠的依据.     

具两系统切换脉冲单种群动力学模型

建立具两系统切换脉冲单种群动力学模型,利用离散动力系统频闪映射理论,得到系统种群灭绝与系统种群持续生存的控制阈值.结果表明脉冲收获与冬眠期对于系统种群持久起着重要作用,从而为现实的生物资源管理与生物多样性保护提供了可靠的策略依据.     

具有脉冲扰动的随机周期单种群扩散模型(英文)

文章研究一个具有脉冲与随机扰动的周期单种群扩散模型.通过构建合适的Lyapunov函数及利用脉冲微分方程比较定理与随机微分方程比较定理,获得种群灭绝和平均持续生存的条件.进而我们确定系统解的均值上界条件.     

一类在污染环境中单种群模型的动力学行为（英文）

在种群的增长率满足广义logistic方程的情况下,建立了在污染环境中一类新的单种群模型,给出了该模型中种群一致持续生存和灭绝的充分条件.这里建立的模型是He和Wang[Appl.Math.Modell.31(2007)2227-2238]中模型的改进.     

具脉冲收获切换单种群动力学模型控制阈值研究

建立具脉冲收获切换单种群动力学模型,利用离散动力系统频闪映射理论,得到系统种群灭绝与系统种群持续生存的控制阈值.结果表明一个周期内适当的二次收获种群对系统种群持久起着重要作用,从而为现实的生物资源管理与生物多样性保护提供了可靠的策略依据.     

在污染环境下带时滞和脉冲输入两种营养液和一种微生物模型性质的研究

提出并研究污染环境下带时滞和脉冲输入的恒化器模型,利用脉冲方程比较定理得到微生物灭绝周期解全局吸引和系统持续生存的充分条件,最后给出一个简单讨论.     

在脉冲污染环境中具有阶段结构的捕食食饵Gompertz模型的动力学性质

研究了在脉冲污染环境中,捕食者具有阶段结构的捕食食饵Gompertz模型的动力学性质,获得了捕食者灭绝周期解全局吸引和系统持续生存的条件.     

在容量较小的污染环境中种群的持续生存与灭绝

本文讨论了在容量较小的污染环境中以广义Logistic形式生长种群动力学性态,得到种群持续生存和灭绝的条件,最后讨论了模型有关平衡点的稳定性。     

一类污染环境中非自治捕食食饵系统的持续生存与灭绝

研究了一类脉冲排放污染环境中受到人类外界干扰作用的非自治捕食食饵系统的动力学性质,利用脉冲微分方程相关理论和分析的方法给出所提出模型的持续生存与灭绝的充分条件.     

Leslie系统在污染环境下有关生存问题的分析

研究了在污染环境中毒素对Leslie资源-消费者系统中消费者种群的长期影响,给出了种群弱持续生存和灭绝的条件．     

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．     

具脉冲出生单种群模型的脉冲收获阈值分析

讨论了与生物资源管理相关的具脉冲出生与脉冲收获的单种群动力学模型,利用离散动力系统频闪映射理论,得到了生物资源管理控制阈值的充分条件.结论为现实的生物资源管理提供了可靠的策略依据,也丰富了脉冲微分方程理论.     

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.     

具脉冲收获与脉冲单边扩散的单种群动力学模型研究

建立了一类具脉冲收获与脉冲单边扩散在不同固定脉冲时刻的单种群动力学模型利用离散动力系统频闪映射理论,得到了脉冲收获的阈值.该结论说明只要收获量不超过其阈值通过扩散则种群可以保持持续生存.     

Evolutionary game dynamics with impulsive effects

The jumps in population size due to the occurrence of an unfavorable physical environment (e.g. the effects of periodic climate disaster on the population size), or due to the intrinsic physiological and reproductive mechanisms of the population (e.g. the seasonal reproduction of most animal populations), can be called impulsive perturbations. A two-phenotype evolutionary game dynamics with impulsive effects is investigated. The main goal is to show how the evolutionary game dynamics is affected by the impulsive perturbations. The results show that the impulsive perturbations not only result in periodic behavior, but also it is possible that an ESS strategy based on the traditional concept of evolutionary stability can be replaced successfully by a non-ESS strategy.     

Research of population with impulsive perturbations based on dynamics of a neutral delay equation and ecological quality system

This paper studies the global behaviors of a nonlinear autonomous neutral delay differential population model with impulsive perturbation. This model may be suitable for describing the dynamics of population with long larval and short adult phases. It is shown that the system may have global stability of the extinction and positive equilibria, or grow without being bounded under some conditions.     

Modelling and analysis of impulsive releases of sterile mosquitoes

To study the impact of releasing sterile mosquitoes on mosquito-borne disease transmissions, we propose two mathematical models with impulsive releases of sterile mosquitoes. We consider periodic impulsive releases in the first model and obtain the existence, uniqueness, and globally stability of a wild-mosquito-eradication periodic solution. We also establish thresholds for the control of the wild mosquito population by selecting the release rate and the release period. In the second model, the impulsive releases are determined by the closely monitored wild mosquito density, or the state feedback. We prove the existence of an order one periodic solution and find a relatively small attraction region, which ensures the wild mosquito population is under control. We provide numerical analysis which shows that a smaller release rate and more frequent releases are more efficient in controlling the wild mosquito population for the periodic releases, but an early release of sterile mosquitoes is more effective for the state feedback releases.     

固定周期脉冲微分方程到状态依赖脉冲的转化及应用

本文研究了一类二维状态依赖脉冲微分方程的阶1周期解存在性和轨道稳定性条件．然后,将一维固定周期脉冲的微分方程转化为二维状态依赖脉冲微分方程,研究其阶一周期解的存在性和稳定性．作为应用,我们研究了固定周期常数收获的Logistic方程的动力学性质,以及两个固定周期注射药物单室扩散模型的动力学性质．     

The prey-dependent consumption two-prey one-predator models with stage structure for the predator and impulsive effects

In this paper, we consider the prey-dependent consumption two-prey one-predator models with stage structure for the predator and impulsive effects. By applying the Floquet theory of linear periodic impulsive equation, we show that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value, that is, the pest population can be eradicated totally. But from the point of ecological balance and saving resources, we only need to control the pest population under the economic threshold level instead of eradicating it totally, and thus, we further prove that the system is uniformly permanent if the impulsive period is larger than some critical value, and meanwhile we also give the conditions for the extinction of one of the two preys and permanence of the remaining species. Thus, we can use the stability of the positive periodic solution and its period to control insect pests at acceptably low levels. Considering population communities always are imbedded in periodically varying environments, and the parameters in ecosystem models may oscillate simultaneously with the periodically varying environments, we add a forcing term into the prey population's intrinsic growth rate. The resulting bifurcation diagrams show that with the varying of parameters, the system experiences process of cycles, periodic windows, periodic-doubling cascade, symmetry breaking bifurcation as well as chaos.     

脉冲浮游生物植化相克模型解的渐近行为

讨论了一类在周期变化环境中的浮游生物植化相克的竞争模型．模型由一个修正的周期系数Lotka-Volterra竞争模型及一些周期脉冲作用条件描述．利用脉冲微分方程的比较原理研究了系统的全局渐近性质,获得了系统持续生存的一组充分条件．