一致渐近稳定和周期解、概周期解的存在性

本文建立了系统解一致稳定、解一致渐近稳定和某种Liapunov函数存在的充要条件,并且得到:满足Lipschitz条件而且解一致渐近稳定的概周期系统有唯一的概周期解,周期系统有唯一的周期解。     

具有扩散率Ayala模型的概周期解

本文研究了非自治Ayala模型的概周期和周期系统,我们得到在一定条件下,其概周期系统存在唯一全局吸引的概周期解且其概周期解在壳扰动下是稳定的。在与概周期情形类似的条件下我们得到其w-周期系统存在唯一全局吸引的w-周期解。     

时不变分数阶系统反周期解的存在性

反周期解问题是非线性微分系统动力学的重要特征.近年来,非线性整数阶微分系统的反周期解问题得到了广泛的研究,非线性分数阶微分系统的反周期解问题也得到了初步的讨论.不同于已有的工作,该文研究时不变分数阶系统反周期解的存在性问题.证明了时不变分数阶系统在有限时间区间内不存在反周期解,而当分数阶导数的下限趋近于无穷大时,时不变分数阶系统却存在反周期解.     

Liénard系统的比较定理

研究了Liénard方程的一类新的等价系统解的有界性与周期解的存在性.证明了几个比较定理,使传统Liénard方程等价系统解的有界性和周期解的存在性可用于判定新等价系统解的有界性与周期解的存在性.     

全局渐近稳定性质与概周期解的存在唯一性

众所周知,周期系统解的有界性蕴含着周期解的存在性。然而对于概周期系统(1)来说,即使在n=1的情况下其解的有界性也未必蕴含着概周期解的存在性。因此,在讨论(1)的概周期解的存在性时,必需同时考虑有界解的某种稳定性质。 本文首先证明当研究概周期系统(1)的概周期解φ(t)的稳定性时,可假设φ(t)是明显解。其次,我们利用李雅普诺夫函数和比较原理得到了(1)的零解为全局等度(均匀)渐近稳定的一些结果。最后,我们亦得到了(1)存在唯一概周期解的充分条件。所得结果推广了[1,11,13]中有关结论。     

一类n维中立型泛函微分方程的周期解

通过对NFDE周期系统；周期解的讨论，给出了其周期解界的估计式，结合不动点原理研究了下列系统：周期解的存在性，唯一性等问题，得到一些新的结果．     

一类单种群系统正周期解及其稳定性

考虑周期单种群模型 dxdt=xg( t,x)± p( t,x)的正周解及其稳定性 .证明了在一定条件下 ,系统存在全局吸引的正周期解 .给出了系统存在两个正周期解的充分条件 ,同时也给出了种群灭绝的条件 .这些结果用于 Logistic模型和 Odum模型 ,得到了被开发的周期 Logistic模型存在全局吸引的正周期解 ;被开发了的周期 Odum模型只存在两个正周期解 ,其中之一吸引初值大于一个定数的所有解 ,另一个周期解则是种群灭绝的分界线     

具有状态反馈脉冲控制的种群互惠动力系统的研究

研究具有状态反馈脉冲控制的种群互惠动力系统.首先利用微分方程几何理论和后继函数的方法得到一般系统阶1周期解的存在条件;然后研究了一类特殊系统,说明了该系统在一定条件下存在唯一的阶1周期解,并且给出了该阶1周期解轨道渐近稳定的条什,此外还探讨了该系统阶2周期解的存在性问题.     

具有Monod-Haldane功能反应和脉冲效应的捕食系统的动力学性质

基于综合害虫防治,对具脉冲效应的Monod—Haldane功能反应的捕食系统进行了分析,根据Floquet乘子理论,获得了害虫灭绝周期解全局渐近稳定与系统持续生存的条件．并讨论了害虫灭绝周期解附近分支出非平凡周期解的问题,且文章利用Matlab软件对害虫灭绝周期解害虫周期爆发现象进行了数值模拟．     

具有限时滞的非自治三种群扩散捕食系统的周期解

主要讨论了具有限时滞的非自治三种群扩散捕食系统的周期解的存在性.方法是运用Yoshizawa型周期解定理的推广,得出该系统至少有一个ω周期解.     

具有扩散和时滞的捕食系统的持续生存

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.     

Dispersal permanence of a periodic predator-prey system with Holling type-IV functional response

In this paper, we study the permanence of a class of periodic predator-prey system with Holling type-IV functional response where the prey disperses in patchy environment with two patches, and provide a sufficient and necessary condition to guarantee permanence of the system. Finally, two examples are presented to illustrate the application of our main results.     

Permanence and extinction for dispersal population systems

This paper studies the effect of dispersal on the permanence of population models in poor patchy environment. We first consider the logistic system with dispersal for single species and obtain the conditions for its permanence. On the basis of the conditions, we then consider a periodic predator-prey system where the prey can disperse among several patches. A necessary and sufficient condition is obtained for the permanence of the periodic predator-prey system. We discuss the biological implications of the main results.     

Uniqueness of periodic solutions of a nonautonomous density-dependent predator–prey system

In this present paper, we investigate the uniqueness of periodic solutions of a nonautonomous density-dependent and ratio-dependent predator–prey system, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator–prey system conforms to the realistically biological environment. We start with a sufficient condition for the permanence of the system and then construct a weaker sufficient condition by introducing a specific set, denoted as Γ. Based on this Γ and the Brouwer fixed-point theorem, we obtain the existence condition of positive periodic solutions. Moreover, since the uniqueness of positive periodic solutions can be ensured by global attractiveness, we alternatively introduce a sufficient condition for global attractiveness. Similarly, we also provide a sufficient condition for the uniqueness of non-negative periodic solutions.     

Permanence of a single-species dispersal system and predator survival

This paper considers permanence of a single-species dispersal periodic system with the possibility of the loss for the species during their dispersion among patches. The condition obtained for permanence generalizes the known condition on the system without loss for the species in the process of movement. Next, we add predators into every patch and consider the survival possibility of the predator. It is shown that the total amount of the predators can remain positive, if the single-species (prey) dispersal system has a positive periodic solution and the quantity of prey in each patch is enough for survival of the predator.     

Permanence, extinction and periodic solution of predator-prey system with Beddington-DeAngelis functional response

In this paper we study permanence, extinction and periodic solution of periodic predator-prey system with Beddington-DeAngelis functional response. We provide a sufficient and necessary condition to guarantee the predator and prey species to be permanent. In addition, sufficient condition is derived for the existence of positive periodic solution. This paper improves some main results obtained by Fan and Kuang [M. Fan, Y. Kuang, Dynamics of nonautonomous predator-prey system with the Beddington-DeAngelis functional response, J. Math. Anal. Appl. 295 (2004) 15-39].     

Existence of periodic solutions in predator-prey with Watt-type functional response and impulsive effects

In this paper, the existence of a periodic solution and the permanence of a periodic Watt-type predator-prey system where the prey disperses in patchy environment with two patches are investigated. With the continuation theorem of coincidence degree theory, we obtain the existence of a positive periodic solution for such a system. We assume the Watt-type functional response within-patch dynamics and provide a sufficient condition to guarantee the predator and prey species to be permanent. Furthermore, we give numerical analysis to confirm our theoretical results. It will be useful to ecosystem control.     

具有脉冲毒素投放和营养再生的恒化器模型

研究具有脉冲毒素投放和营养再生的恒化器模型.利用脉冲微分方程的比较定理和小扰动方法得到了边界周期解全局渐近稳定的充分条件,进而得到了系统持续生存的充分条件.结果表明毒素环境将会导致微生物种群的灭绝.     

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

In this paper, we concentrates on the study of a single stage-structured population model with mature individuals in a polluted environment and pulse input of environmental toxin. A globally attractive condition for the population-extinction boundary periodic solution of the investigated system is obtained. Sufficient criteria on the permanence of the population are derived.     

基于脉冲控制的害虫管理数学模型研究

研究一类害虫管理SI传染病模型,考虑脉冲投放病虫和人工捕杀相结合,得到系统的灭绝周期解,给出此周期解的全局吸引性,并获得了系统一致持续生存的条件.给出了害虫管理综合防治策略.