一个概周期锁相环路方程的概周期解的存在唯一性和渐近稳定性

本文研究了一个概周期锁相环路方程的概周期解的存在唯一性及渐近稳定性,得到了保证系统存在唯一渐近稳定的概周期解的充分条件     

ON ALMOST PERIODIC SOLUTIONS OF AHIGHER ORDER ALMOST PERIODIC SYSTEM

1IntroductionConsiderthel'Ollowingdifferentialequationdx~~A(.t)x g(t,x),(l)dt.wherexeR",t6R,A(t)=(a,,(t)),,..istillnxncontinlloust'llllctiollmatrixinR,g(t,x)isanat-dimensionalcolltinuousfunctionvectorinRxR".Thepaper[l,21dealedwil;htheproblemontheexistence…     

PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF A NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURE AND DELAY

In this paper, by using the comparing theorem, Razumikhin-type theorem and V-function method, we consider a nonautonomous predator-prey system with stage-structure and time-delay. We get the sufficient conditions for the uniform persistence and the solutions global attractivity of this system. For a periodic system, we obtain the existence and uniqueness of a positive periodic solution of this system. For an almost periodic system, we prove the existence and the uniform asymptotic stability of the almost periodic solutions of this system.     

PERIODIC SOLUTION AND ALMOST PERIODIC SOLUTION OF NONAUTONOMOUS COMPETITIVE MODEL WITH STAGE STRUCTURE AND HARVESTING

In this paper, a two-species nonautonomous competitive model with stage structure and harvesting is considered. Sufficient conditions for the existence, uniqueness, global attractivity of positive periodic solution and the existence, uniform asymptotic stability of almost periodic solution are obtained.     

Global dynamics behaviors for a nonautonomous Lotka–Volterra almost periodic dispersal system with delays

A nonautonomous Lotka–Volterra dispersal system with continuous delays and discrete delays is considered. By using a comparison theorem and delay differential equation basic theory, we obtain sufficient conditions for the permanence of the population in every patch. By constructing a suitable Lyapunov functional, we prove that the system is globally asymptotically stable under some appropriate conditions. Using almost periodic functional hull theory, we get sufficient conditions for the existence, uniqueness and globally asymptotical stability for an almost periodic solution. This implies that the population in every patch exhibits stable almost periodic fluctuation. Furthermore, the results show that the permanence and global stability of system, and the existence and uniqueness of a positive almost periodic solution, depend on the delay; then we call it “profitless”.     

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.     

比率型-捕食者-两竞争食饵模型的动力学行为

本文研究比率型非自治的捕食者 -食饵模型 .该系统是两个具有竞争关系的食饵种群被一个捕食种群捕食 .我们研究其动力学行为 ,包括持久性 ,全局渐近稳定性 ,周期解 ,概周期解的存在唯一性     

捕食者一食Lotka—Volterra系统的概周期解

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．     

捕食者-食Lotka-Volterra系统的概周期解(英文)

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.     

ON THE EXISTENCE OF PERIODIC SOLUTION OF HIGHER ORDER PERIODIC SYSTEM

ＯＮＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＨＩＧＨＥＲＯＲＤＥＲＰＥＲＩＯＤＩＣＳＹＳＴＥＭ（王全义）华侨大学，邮编：３６２０１１ＷａｎｇＱｕａｎｙｉ（ＨｕａｑｉａｏＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐ...     

ON THE ALMOST PERIODIC SOLUTIONS OF HIGHER DIMENSIONAL NONAUTONOMOUS SYSTEMS

By means of the properties of almost periodic system and Lyapunov function, we give some criteria which guarantee the existence and uniqueness and stability of almost periodic solutions of higher dimensional nonautonomous system. The result is more convenient and effective than the related result in[1].     

A NONAUTONOMOUS STAGE-STRUCTURED SINGLE SPECIES MODEL WITH DIFFUSION

1IntroductionRecent1ytheso-calledsinglespeciesm0delwasconsidered,andmanyrcsultshavebeen.bt.in.d[1-7J.In[l],thesinglespeciesmodelwithstage-structtlredinthefOrmofisstudied,whereIi(t)andx.(t)representtheimmatureandmaturepopu-lati0nsdensitiesrespectively;ofisthe0bservedorassumedbirthrateofxi(t)attimet(-T5t5O),andTrepresentsac0nstanttime1engthfortheiITl-maturetobecomematurity.aisthebirthrateofmaturepopulation.7isthedeathrateofimmaturepopulationandfiistheLogisticconstantofthemature.Somesufficien…     

一类非线性时滞系统概周期解的存在唯一性

应用Liapunov，泛函，研究了一类时滞系统概周期解的存在唯一性，得到了保证系统存在唯一概周期解的一组充分条件．     

一类非自治随机微分方程的均方渐近概周期解

本文研究了一类在可分Hilbert空间中的非自治随机微分方程的均方渐近概周期解.利用"Acquistapace-Terreni"条件,开方族和Banach不动点原理讨论了该类随机微分方程的均方渐近概周期解的存在唯一性,推广了该类随机微分方程的均方概周期解的存在唯一性问题.     

THE EXISTENCE AND UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

ＴＨＥＥＸＩＳＴＥＮＣＥＡＮＤＵＮＩＱＵＥＮＥＳＳＡＮＤＳＴＡＢＩＬＩＴＹＯＦＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＦＯＲＦＵＮＣＴＩＯＮＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＩＮＦＩＮＩＴＥＤＥＬＡＹＳＷＡＮＧＱＵＡＮＨＮＹ...     

具无穷时滞的中立型Volterra积分微分方程的概周期解

研究了一类具无穷时滞的中立型Volterra积分微分方程的概周期解问题．利用线性系统指数型二分性理论和泛函分析方法,得到了一些关于该方程的概周期解的存在性、唯一性与稳定性的新结果,推广了相关文献的主要结果．     

Existence and global exponential stability of almost periodic solution for quaternion-valued high-order Hopfield neural networks with delays via a direct method

This paper deals with the existence and global exponential stability of almost periodic solutions for quaternion-valued high-order Hopfield neural networks with delays by a direct approach. Based on the contraction mapping principle, sufficient conditions are derived to ensure the existence and uniqueness of almost periodic solutions for the networks under consideration. By constructing a suitable Lyapunov function, the global exponential stability criterion of the almost periodic solution are derived. Finally, two numerical examples are given to illustrate the main results of this paper.     

On the module containment of the almost periodic solution for a class of differential equations with piecewise constant delays

In the first part of this paper, we obtain a new property on the module containment for almost periodic functions. Based on it, we establish the module containment of an almost periodic solution for a class of differential equations with piecewise constant delays. In the second part, we investigate the existence, uniqueness and exponential stability of a positive almost periodic and quasi-periodic solution for a certain class of logistic differential equations with a piecewise constant delay. The module containment for the almost periodic solution is established.     

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.     

一类非线性系统周期解的存在唯一性及其渐近性态

利用Liapunov函数方法,研究了一类一般的非线性系统周期解的存在唯一性与渐近稳定性,得到了存在唯一渐近稳定周期解的充分条件。