高维时滞周期的Kolmogorov型系统的正周期解

本文应用Ｂａｎａｃｈ空间中的Ｈｏｒｎ不动点得到了高维时滞的周期Ｋｏｌｍｏｇｏｒｏｖ型生态系统的正周期解存在性定理,作为这个定理的应用,讨论了几类时滞的周期ＬｏｔｋａＶｏｌｔｅｒｒａ型系统的正周期解的存在性问题,建立了新的实用的判别准则。     

周期参数扰动的T混沌系统周期轨道分析

本文研究了一类周期参数扰动的T混沌系统的周期轨道问题.利用次谐波Melnikov方法,获得了具有广义Hamilton结构的周期参数扰动的慢变系统的振荡周期轨道和旋转周期轨道.     

一个A（f）≠M（f）的紧致系统（X，f）

本文证明，存在紧致系统，其几乎周期点集闭包不等于其测度中心．藉此，我们否定地回答了两个未解决的问题．     

带有Leslie-Gower功能性反应的三维食物链模型研究

研究了离散时间上带有Leslie-Gower功能性反应的三维食物链模型.首先给出保证系统永久持续生成的条件,由于系统系数的周期性,正周期解是存在的,最后通过在正的周期解领域内线性化系统,并通过构造Lyapunov函数,我们得出了保证系统正周期解全局稳定的条件.     

具有脉冲效应和综合害虫控制的捕食系统

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.     

一种具有脉冲扰动的恒化器模型的动力学性质

在这篇文章中,我们提出并分析了一个具有捕食者,食饵和既有周期脉冲输入又有周期脉冲输出营养液的恒化器模型.我们得到了一种微生物和营养液共存的周期解,同时,也得到两种微生物都绝灭的周期解,而且建立了周期解稳定的充分条件.最后,我们给出了一个简单的讨论.     

碰振系统中的共存周期轨道

提出一种寻找分段线性碰振系统中的多个周期轨道共存的分析方法,这些单碰周期轨道包含稳定的和不稳定的轨道。给出了单碰周期轨道存在性或不存在性的解析判别式,特别是对如何保证在单碰周期运动中不会发生其它的碰撞的问题作了比较深入的研究,得到若干定理。最后讨论了所得共存周期轨道的稳定性问题,获得了稳定性的判别式。还以数值模拟结果验证了理论分析的结论。     

具无穷时滞的中立型周期微分系统周期解的存在性

研究了一类具无穷时滞的中立型周期微分系统周期解的存在性问题.利用指数型二分性及Krasnoselskii不动点定理,建立了保证该系统的周期解的存在性的充分条件.所得结果推广了文[1-7]的有关结果.     

离散Leslie捕食与被捕食系统周期解的稳定性

该文讨论了一类离散Leslie捕食与被捕食系统,获得了该系统的持久性,当系统为周期系统时,得到了它的周期解的存在性,并且在某些条件下,该周期解是全局稳定的.     

A threshold policy to curb WNV transmission to birds with seasonality

Seasonality is pervasive in nature and WNV is a complex disease which appears to be transmitted periodically. Lacking of vaccine and anti-virus treatment brings culling to be an effective strategy of controlling the spread of WNV. This paper proposes a piecewise smooth model of WNV transmission between mosquitoes and birds with periodic forcing by employing the threshold policy of culling mosquitoes and birds when the number of infected birds exceeds the critical level. We firstly investigate the dynamical behaviours of the periodic subsystems and illustrate the existence and global stability of the disease-free and positive periodic solutions. Then by assuming a periodic variation in the total number of mosquitoes and birds with and without culling strategy respectively in the ecosystem, the subsystems are reduced, respectively. Further, the sliding mode domain and sliding mode dynamics are derived by using the Filippov convex method and the existence of the sliding periodic solution is illustrated. Finally, numerical investigations are carried out to address how the periodic forcing and culling strategy affect the pattern and amplitude of the novel periodic solution. Our results show that a suitable combination of threshold value and culling rates should be properly chosen to ensure that the ideal periodic solution with a low number of infected birds/mosquitoes oscillating in a small range is globally stable and consequently is approximated, which suggests useful strategies of curbing WNV transmission by setting proper threshold level and culling rates.     

Multiple periodic oscillations in a nonlinear suspension bridge system

In this paper, we study periodic oscillations in a suspension bridge system governed by the coupled nonlinear wave and beam equations describing oscillations in the supporting cable and roadbed under periodic external forces. By applying a variational reduction method, it is proved that the suspension bridge system has at least three periodic oscillations.     

On the well-posedness of periodic problems for the system of hyperbolic equations with finite time delay

A periodic problem for the system of hyperbolic equations with finite time delay is investigated. The investigated problem is reduced to an equivalent problem, consisting the family of periodic problems for a system of ordinary differential equations with finite delay and integral equations using the method of a new functions introduction. Relationship of periodic problem for the system of hyperbolic equations with finite time delay and the family of periodic problems for the system of ordinary differential equations with finite delay is established. Algorithms for finding approximate solutions of the equivalent problem are constructed, and their convergence is proved. Criteria of well-posedness of periodic problem for the system of hyperbolic equations with finite time delay are obtained.     

具有无限时滞的中立型高维周期微分系统的周期解

本文考虑中立型高维周期微分系统d/dt(x(t)+cx(t-r))=A(t,x(t-r(t)))x(t)+ ∫t-∞C(t,s)x(s)ds+f(t,xt)+b(t)的T-周期解的存在性问题,利用线性系统的指数型 二分性和Krasnoselskii不动点定理,建立了保证系统存在T-周期解的充分条件.     

GLOBAL ASYMPTOTIC STABILITY OF PERIODIC SOLUTION IN N-SPECIES COMPETITION SYSTEM WITH TIME DELAYS

１ＩｎｔｒｏｄｕｃｔｉｏｎＩｔｉｓｋｎｏｗｎｔｈａｔｍｅｔｈｏｄｓｏｆｍａｔｈｅｍａｔｉｃａｌｍｏｄｅｌｃａｎｂｅｕｓｅｄｔｏｄｅｓｃｒｉｂｅｔｈｅｄｙｎａｍｉｃａｌｂｅｈａｖｉｏｒａｍｏｎｇｓｐｅｃｉｅｓｉｎｅｃｏｌｏｇｙ．Ｒｅｃｅｎｔｌｙｍａｎ...     

Global dynamics of the periodic logistic system with periodic impulsive perturbations

This paper studies the global behaviors of the periodic logistic system with periodic impulsive perturbations. The results of D.D. Bainov and P.S. Simeonov (1993) are extended and dynamics different from the corresponding continuous system are found. It is shown that the system may have a unique positive periodic solution which is globally asymptotically stable, or go extinct when the two periods are rational dependent. When they are rational independent, the system has no periodic solutions, however, still has a global attractor or go extinct under some conditions.     

一类状态反馈脉冲控制的捕食者-食饵动力系统

本文研究了具有状态反馈脉冲控制的一类捕食者-食饵动力系统.我们首先利用微分方程几何理论和后继函数的方法得到该系统阶1周期解的存在性、唯一性和轨道渐近稳定性;然后说明了该系统不存在阶k(k=2,3,…)周期解,最后简单分析了相关结论在实践中的应用.     

Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response

In this paper, we systematically study the dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response. The explorations involve the permanence, extinction, global asymptotic stability (general nonautonomous case); the existence, uniqueness and stability of a positive (almost) periodic solution and a boundary (almost) periodic solution for the periodic (almost periodic) case. The paper ends with some interesting numerical simulations that complement our analytical findings.     

具有反馈控制的离散两种群竞争系统的概周期解

对于具有反馈控制的离散概周期两种群竞争系统的概周期解问题,进行了深入的讨论,得到了该系统存在唯一的一致渐近稳定概周期解的充分条件.     

具有脉冲效应的周期三种群捕食-食饵系统

本文讨论一类具有脉冲效应和周期系数的两个食饵一个捕食者的捕食-食饵系统的动力学行为.利用脉冲微分方程比较定理和乘子理论,证明了系统的有界性,讨论了平凡周期解和半平凡周期解的稳定性,利用重合度的理论给出了系统存在周期正解的充分条件.     

A model for assisted periodic breathing with degenerate permeability

The process of breathing is interpreted as forced periodic motion of a viscoelastic deformable porous medium with gas exchange between the interior and exterior, driven by forces acting on its boundary. Energy and mass are supplied to the system by muscle activity, and also possibly by external ventilation in case of assisted breathing for patients with lungs insufficiency. Hysteresis in the pressure–volume characteristic and possible degeneracy of the pressure-dependent terms are also taken into account. The main result consists in proving the existence of a periodic solution under arbitrary periodic forcing in suitable function spaces.