周期系数三种群Lotka—Volterra混合模型分析

考虑三种群Ｌｏｔｋａ－Ｖｏｌｔｅｒｒａ周期系数模型，种群间既有捕食关系又有竞争关系，得到唯一存在全局渐近稳定周期解的条件，并举例文明条件的可行性。     

三种群Lotka-Volterra周期系数混合模型的全局渐近稳定性

本文考虑周期系数的三种群 Lokta-Volterra模型 ,种群间既有捕食关系又有竞争关系 ,得到其正周期解的存在性及其全局渐近稳定性的条件 ,且举例说明条件的可行性     

三种群L0tka-V0lterra周期系数混合模型的全局渐近稳定性

本文考虑周期系数的三种群Lokta-Volterra模型,种群间既有捕食关系又有竞争关系,得到其正周期解的存在性及其全局渐近稳定性的条件,且举例说明条件的可行性.     

由分式线性递归关系所确定的周期数列

由分式线性递归关系所确定的周期数列薛布群（陕西兴平南位高中７１３１００）本文目的在于探求分式线性递归关系，ｔ为常数，且在给定初始值ｘ１＝ｘｏ后所构成的数列为周期数列（非常数列）的条件．设是递补归数列为常数，且的特征方程入的两个根．１．当时，可以得到因...     

五种群Lotka-Volterra混合系统的全局渐近稳定性

考虑周期系数的五种群Lotka-Volterra模型,种群间既有捕食关系又有竞争关系,得到该系统的正周期解的存在性及全局渐近稳定性的条件.     

带有时滞的非自治三种群Lotka-volterra混合模型的渐近性

讨论非自治的周期系数的Lotka-volterra三种群时滞混合摸型,种群间既有捕食关系又有竞争关系,当系数满足一定条件时模型的持久性,进而获得了模型正周期解存在与全局渐近稳定的充分条件,并举例说明条件的可行性.     

一类拟线性系统的Lyapunov不等式

本文研究了一类拟线性系统，引入了反周期边值条件，基于反周期边值条件和数学分析的技巧，建立了新的Lyapunov不等式．     

函数中六类“特殊点”的关系

在中学阶段，周期数列问题的一般解法是列举前有限项观察其周期性，再利用其周期求解，显然，列举前有限项的方法只能解决一些最小正周期不大的数列问题，对于最小正周期较大的数列我们就不易解决了，而且，由数列的前有限项来得出它是周期数列的结论也缺乏科学证明，笔者在数列内容的教学中，总结了三类周期数列及三个结论，它们的递推关系比较特殊，我们可以通过其递推关系直接判断周期，从而解决相关问题。     

拓扑Markov链——非游荡集和拓扑熵

本文讨论了拓扑Markov链,给出了涉及拓扑熵、紊动点偶、ω-极限集、非游荡集、周期点集和终于周期点集之间关系的7个等价条件。     

具周期输入的有限连续分布时滞神经网络周期解的全局指数稳定性

在去掉对激励函数有界、连续可导、平均时滞有界的条件下,仅要求激励函数满足Lip-schitz条件和连接权矩阵之间的关系是一个M-矩阵的情形下,利用重合度理论、Dini导数等知识得出了具周期输入的有限连续分布的一类细胞神经网络周期解的存在性.利用Dini导数和不等式分析技术在同样条件下得出了周期解的指数稳定性.推广和改进了前人的结论.并举例说明了所得定理的有效性.     

Periodic jordan rings and order structure

The aim of this paper is to obtain information about a periodic Jordan ring by using only properties of its idempotent elements. Osborn proves that a power-associative periodic ring having only one nonzero idempotent element is a division ring. so associative. He also proves that a periodic Jordan ring is a subdirect product of simple periodic Jordan rings and that a simple periodic Jordan ring is either a periodic field or a Jordan ring of capacity 2. Using these results we obtain some necessary and suficient conditions for a periodic Jordan ring to be associative, and these conditions are only given in terms of the idempotent elements. We also characterize the periodic Jordan ring which are a direct product of periodic fields and simple periodic Jordan rings of capacity two.     

Approximation of Periodic Solutions of a System of Periodic Linear Nonhomogeneous Differential Equations

The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid.     

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     

Quadratic control for linear periodic systems

We propose a new quadratic control problem for linear periodic systems which can be finite or infinite dimensional. We consider both deterministic and stochastic cases. It is a generalization of average cost criterion, which is usually considered for time-invariant systems. We give sufficient conditions for the existence of periodic solutions.Under stabilizability and detectability conditions we show that the optimal control is given by a periodic feedback which involves the periodic solution of a Riccati equation. The optimal closed-loop system has a unique periodic solution which is globally exponentially asymptotically stable. In the stochastic case we also consider the quadratic problem under partial observation. Under two sets of stabilizability and detectability conditions we obtain the separation principle. The filter equation is not periodic, but we show that it can be effectively replaced by a periodic filter. The theory is illustrated by simple examples.This work was done while this author was a visiting professor at the Scuola Normale Superiore, Pisa.     

The necessary and sufficient conditions for the existence of periodic orbits in a Lotka-Volterra system

By extending Darboux method to three dimension, we present necessary and sufficient conditions for the existence of periodic orbits in three species Lotka-Volterra systems with the same intrinsic growth rates. Therefore, all the published sufficient or necessary conditions for the existence of periodic orbits of the system are included in our results. Furthermore, we prove the stability of periodic orbits. Hopf bifurcation is shown for the emergence of periodic orbits and new phenomenon is presented: at critical values, each equilibrium are surrounded by either equilibria or periodic orbits.     

Asymptotic behavior of solutions of a periodic diffusion system of plankton allelopathy

This paper is concerned with the existence and asymptotic behavior of periodic solutions for a periodic reaction diffusion system of a planktonic competition model under Dirichlet boundary conditions. The approach to the problem is by the method of upper and lower solutions and the bootstrap argument of Ahmad and Lazer. It is shown under certain conditions that this system has positive or semi-positive periodic solutions. A sufficient condition is obtained to ensure the stability and global attractivity of positive periodic solutions.     

具有饱和项的捕食食饵系统正周期解的存在性

By the theory of periodic parabolic operators, Shauder estimates and bifurcation, the existence of positive periodic solutions for periodic prey-predator model with saturation is discussed. The necessary and sufficient conditions to coexistence of periodic system are obtained.     

共振条件下一类方程无界解和周期解的共存性

讨论了在共振条件下一类具有等时位势的方程无界解和周期解的共存性．利用Poincare映射轨道的性质,给出了无界解的存在性条件．在此条件下,Poincare-Bohl定理,得到了方程的一个周期解,进而说明共振条件下这类方程无界解和周期解的是可以共存的．最后,给出了一个无界解和周期解共存的具有等时位势的方程实例．     

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.     

Periodic and almost periodic solution for a non-autonomous epidemic predator-prey system with time-delay

In this paper, we studied a non-autonomous predator-prey system with discrete time-delay, where there is epidemic disease in the predator. By using some techniques of the differential inequalities and delay differential inequalities, we proved that the system is permanent under some appropriate conditions. When all the coefficients of the system is periodic, we obtained the existence and global attractivity of the positive periodic solution by Mawhin’s continuation theorem and constructing a suitable Lyapunov functional. Furthermore, when the coefficients of the system are not absolutely periodic but almost periodic, sufficient conditions are also derived for the existence and asymptotic stability of the almost periodic solution.