一类具有反馈控制和Holling-Ⅲ类功能性反应的比率依赖离散时滞模型的持久性

主要讨论一类基于比率的具有反馈控制变量的Holling-Ⅲ离散模型,通过运用差分不等式的有关结论和一些计算技巧,得到了保证该系统持久性的充分性条件,数值模拟也证明结论是可行的.     

异结构离散型混沌系统的延迟同步

以异结构离散型混沌系统为研究对象,设计了一种延迟同步控制器实现了离散型Henon混沌系统和Ikeda混沌系统之间的同步控制．根据稳定性定理,确定了延迟同步控制器的结构以及系统状态变量之间的误差方程．设计的延迟同步控制器对于不同的离散型混沌系统具有统一的形式,可以实现任意异结构离散型混沌系统之间的延迟同步．数值仿真模拟进一步验证了该控制器的有效性．     

模糊有穷自动机的互模拟关系

互模拟是离散事件系统中的一个等价关系,它已经应用到概率、随机和加权自动机中.本文给出模糊有穷自动机(FFA)前向互模拟关系和后向互模拟关系的定义,并给出它们的一些性质,证明前向和后向互模拟关系对于模糊有穷自动机(FFA)的一些运算(并,连接,交)和模糊正则语言的表现定理是封闭的.另外文中还给出一个可在有限步计算极大前向互模拟关系的算法,最后指出前向和后向互模拟之间的区别.     

以中心- 迎风数值格式研究具有外力项的p 系统

本文以半离散中心- 迎风数值格式研究具有外力项的p 系统. 中心型数值格式用来处理双曲型守恒律或系统的优势是快速且简单, 因为不需要使用近似Riemann 解, 也不需要做特征分解. 我们的数值模拟验证了理论研究结果: 具有外力项的p 系统的解的收敛及爆破行为, 同时也指出一些尚待理论研究的问题.     

离散大系统关于部分变元的稳定性和有界性

本文利用文献[1—4]中大系统的分解理论及Lyapunov函数的加权,讨论了离散大系统关于部分变元的稳定性与有界性,得到了一些新的结果. 考虑由下列形式方程描述的离散时间系统:     

直接数值模拟／大涡模拟中数值误差影响的研究

通过比较湍流的能谱和总动能,对数值误差(包括混淆误差、离散截断误差)、亚格子模型以及它们之间相互作用对直接数值模拟和大涡模拟的影响进行了系统研究.算例采用了三维各向均匀同性湍流.为了研究复杂几何形状,数值格式采用了谱方法和Pade紧致格式.大涡模型采用了truncated Navior-Stokes(TNS)模型结合Pade离散滤波器.结果表明直接数值模拟中离散误差对结果有很大影响,低阶格式会导致计算发散.而大涡模拟中亚格子模型不仅能表征小尺度对大尺度的影响,而且还缓解了数值误差对计算结果的影响.因而低精度格式也可取得不错的结果.     

离散Leslie—Gower型捕食与被捕食系统的Neimark—Sacker分岔

本文利用映射的分岔理论讨论了离散Leslie—Gower型捕食与被捕食系统的Neimark—Sacker分岔,并通过数值模拟验证了所得结果的正确性。     

离散哈密顿系统多个周期解的存在性

本文利用临界点理论,建立了一类离散哈密顿系统存在多个周期解的一些充分条件.     

一类Lotka—Volterra型捕食与被捕食系统的Flip分岔

本文利用中心流形定理和映射的分岔理论,研究了一类离散的捕食与被捕食系统的Flip分岔的存在性与稳定性,并给出了数值模拟的结果。     

非线性半离散森林系统的稳定性

讨论森林发展系统的一类非线性林龄面积结构的半离散模型 ,给出了非线性半离散系统稳定的一些充分条件 .     

Existence of positive periodic solution for ratio-dependent N-species difference system

In this paper, we propose a food web model consisting of n-1$n-1$ competing preys and one predator. Firstly, following the same idea and method in [M. Fan, K. Wang, Periodic solutions of discrete time nonautonomous ratio-dependent predator–prey system, Math. Comput. Model. 35 (2002) 951–961], we derive the discrete time analogue of the model. Then, the easily verifiable sufficient criteria are established for the existence of positive periodic solutions of this analogue, the approach is based on the coincidence degree and the related continuation theorem as well as some prior estimates. Meanwhile, some numerical simulations are carried out to support the theoretical analysis of the research.     

Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system

With the help of differential equations with piecewise constant arguments, we first propose a discrete analogue of continuous time ratio-dependent predator-prey system, which is governed by nonautonomous difference equations, modeling the dynamics of the prey and the predator having nonoverlapping generations. Then, easily verifiable sufficient criteria are established for the existence of positive periodic solutions. The approach is based on the coincidence degree and the related continuation theorem as well as some priori estimates.     

Three-dimensional discrete-time Lotka–Volterra models with an application to industrial clusters

We consider a three-dimensional discrete dynamical system that describes an application to economics of a generalization of the Lotka–Volterra prey–predator model. The dynamic model proposed is used to describe the interactions among industrial clusters (or districts), following a suggestion given by [23]. After studying some local and global properties and bifurcations in bidimensional Lotka–Volterra maps, by numerical explorations we show how some of them can be extended to their three-dimensional counterparts, even if their analytic and geometric characterization becomes much more difficult and challenging. We also show a global bifurcation of the three-dimensional system that has no two-dimensional analogue. Besides the particular economic application considered, the study of the discrete version of Lotka–Volterra dynamical systems turns out to be a quite rich and interesting topic by itself, i.e. from a purely mathematical point of view.     

On a stoichiometric two predators on one prey discrete model

In this letter, we first propose a discrete analogue of a continuous time predator–prey system, which models the dynamics of two predators on one prey [I. Loladze, Y. Kuang, J. Elser, W.F. Fagan, Competition and stoichiometry: Coexistence of two predators on one prey, Theor. Popul. Biol. 65 (2004) 1–15]. Then, we study the dynamics of this discrete model. We establish results on boundedness and global attractivity. Finally, several numerical simulations are given to support the theoretical results.     

Difference Equations and Discriminants for Discrete Orthogonal Polynomials

We prove that any set of polynomials orthogonal with respect to a discrete measure supported on equidistant points contained in a half line satisfy a second order difference equation. We also give a discrete analogue of the discriminant and give a general formula for the discrete discriminant of a discrete orthogonal polynomial. As an application we give explicit evaluations of the discrete discriminants of the Meixner and the Hahn polynomials. A difference analogue of the Bethe Ansatz equations is also mentioned.Research partially supported by NSF grant DMS 99-70865     

K-amenability for amalgamated free products of amenable discrete quantum groups

The basic notions and results of equivariant KK-theory concerning crossed products can be extended to the case of locally compact quantum groups. We recall these constructions and prove some useful properties of subgroups and amalgamated free products of discrete quantum groups. Using these properties and a quantum analogue of the Bass-Serre tree, we establish the K-amenability of amalgamated free products of amenable discrete quantum groups.     

Conformal hexagonal meshes

We explore discrete conformal and discrete minimal surfaces whose faces are planar hexagons throughout. Discrete conformal meshes are built of conformal hexagons for which we establish a dual construction. We apply this dual construction to conformal hexagonal meshes covering the sphere and get discrete hexagonal minimal surfaces via a discrete analogue to the Christoffel dual construction. We compare the smooth and the discrete settings by means of limit considerations and also by a discussion of Möbius invariants.     

一类非线性差分人口模型解的全局渐近稳定性

考虑非线性差分方程其中a＞0，b≤0，c＞0．方程（1）是时滞人口模型的离散模拟．J．W．Rodrigus[7]研究了方程（1）当k＝0时正平衡解的振动性和全局渐过稳定性．本文我们获得了方程（1）当k＞0时正平衡解全局渐近稳定的充分条件，从而补充了文[7]中结论．     

On discrete unimodality

Characterizations of discrete unimodality are studied. They are applied to prove some criteria for characteristic functions of discrete unimodal distributions and to obtain a discrete analogue of the Gauss inequality. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia. 1996. Part II.     

Regularity of Harmonic Functions for Some Markov Chains with Unbounded Range

We consider a class of continuous time Markov chains on ? ^d . These chains are the discrete space analogue of Markov processes with jumps. Under some conditions, as we show, harmonic functions associated with these Markov chains are Hölder continuous.