某类差分方程零解的全局吸引性及其应用

研究差分方程△xn=r n f(x n-k)的全局吸引性），用二次迭代法导出方程的零解全局吸引的一族新的充分条件，将结果应用于Logistic差分方程及Michelis-Menten差分模型，所得推论改进了已有结果。     

具反馈控制的多滞量Logistic增长模型的全局吸引性

本文研究具反馈控制的多滞量Logistic增长模型的全局吸引性.所得结果改善并推广了一些已知定理.     

具反馈控制的多滞量Logistic增长模型的全局吸引性

本文研究具反馈控制的多滞量Ｌｏｇｉｓｔｉｃ增长模型的全局吸引性．所得结果改善井推广了一些已知定理．     

含阶段结构的单种群模型正周期解的存在性与全局吸引性

研究了具有阶段结构的非自治单种群模型.运用叠合度定理和Lyapunov函数的方法,得到了模型的正周期解的存在性和全局吸引性的充分条件.     

一类具有年龄和病程的SEIR传染病模型无病平衡解分析

研究一类具有年龄和病程的SEIR传染病模型.利用特征线方法、Lebesgue控制收敛定理对无病平衡解的渐近性进行了分析,证明了当R1时无病平衡解是全局渐近吸引的.     

具有遗传效应单种群模型的正周期解

利用重合度理论中的延拓定理和Ｌｙａｐｕｎｏｖ泛函方法,讨论了具有遗传效应单种群模型正周期解的存在性和全局吸引性,得到了一些新结果,推广了某些相关结果。     

有时滞的差分Nicholson''s Blowflies模型的持久性和全局吸引性

本文研究了一类具有时滞的差分Nicholson''s Blowflies模型. 通过构造适当的Lyapunov泛函,得到了系统一致持久和全局吸引性的一组充分性条件．例子和数值模拟说明了我们结果的可行性．     

差分方程x_(n 1)=x_ne~r·((1-ax_n)/(1-bx_n))的全局吸引性

本文讨论差分方程的全局吸引性．证明了当时，*是全局吸引的．     

一类化学模型的确定模式和分形维数（英文）

本文研究一类化学模型解半群全局吸引子的解构,估计了全局吸引子上轨道的确定模式,同时估计了全局吸引子的分形维数有限.     

具有脉冲和时滞的Logistic模型的持续生存和正周期解的全局吸引性(英文)

本文研究了具有脉冲和时滞效应的Logistic模型.利用脉冲微分方程的比较定理,BohlBrower不动点定理和Lyapunov函数法,获得了系统持续生存,正周期解存在、唯一以及全局吸引的充分条件.结果表明正周期解的全局吸引性与时滞有关.     

A sharp global stability result for a discrete population model

We get a sharp global stability result for a first order difference equation modelling the growth of bobwhite quail populations. The corresponding higher-dimensional model is also discussed, and our stability conditions improve other recent results for the same equation.     

Teaching the computer how to discover(!) and then prove(!!) (all by itself(!!!)) analogues of Collatz's notorious 3x + 1 conjecture

In this paper, we study the global attractivity for a class of periodic difference equation with delay which has a generalized form of Pielou's difference equation. The global dynamics of the equation is characterized by using a relation between the upper limit and lower limit of the solution. There are two possible global dynamics: zero solution is globally attractive or there exists a periodic solution which is globally attractive. Recent results by Camouzis and Ladas [Periodically forced Pielou's equation, J. Math. Anal. Appl. 333 (1) (2007) 117–127] are generalized. Two examples are given to illustrate our results.     

一类非线性差分方程的持续生存与全局吸引

研究了非线性差分方程xn 1=x^snf(xn,xn-k,…,xn-kr)s∈{1,2,…}得到该系统永久持续生存和全局吸引的充分条件。     

THE GLOBAL DUFORT-FRANKEL DIFFERENCE APPROXIMATION FOR NONLINEAR REACTION-DIFFUSION EQUATIONS

1.IntroductionInthispaperweconsiderthefollowinginitial-valueproblemofnonlinearreactiondiffusionequation:HerefiisaboundeddomaininRd(d<3)withaLipschitzboundaryOffand7isapositiveconstallt.Lettheset{in*l:j(u*)=0}benotemptyandu=ma-c{lu*I:f(u*)=0}.Assumptionont…     

Global attractivity of a unique positive periodic solution for a first-order nonlinear difference equation with time delays

The present paper is directed toward the study on the global attractivity of a unique positive periodic solution of a discrete hematopoiesis model with unimodal production functions and several time delays. This model is described by a nonlinear difference equation. The result obtained is proved by transforming this model into another difference equation and by using the Schauder fixed-point theorem.     

EXISTENCE OF POSITIVE SOLUTIONS AND 1/c-GLOBAL ATTRACTIVITY OF A NONLINEAR DELAY DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

§ 1　IntroductionConsider the difference equationΔyn=rnynK -yn- ln K -cyn- ln,　 n =0 ,1 ,2 ,...,( 1 .1 )whereΔ is the forward difference operator defined byΔyn=yn+1 -yn,{rn}n≥ 0 is a sequenceof nonnegative real numbers,{ln}n≥ 0 is a sequence of positive integers,{n-ln}n≥ 0 is nonde-creasing,limn→∞ ( n-ln) =∞ ,and K is a positive constant,c∈ [0 ,1 ) .Obviously,( 1 .1 ) is aformally discrete analogue of the following single population growth model:N′( t) =r( t) N( t) K -N( t-τ( t…     

Local and global Hopf bifurcation in a neutral population model with age structure

In this paper, an age‐structured population model with the form of neutral functional differential equation is studied. We discuss the stability of the positive equilibrium by analyzing the characteristic equation. Local Hopf bifurcation results are also obtained by choosing the mature delay as bifurcation parameter. On the center manifold, the normal form of the Hopf bifurcation is derived, and explicit formulae for determining the criticality of bifurcation are theoretically given. Moreover, the global continuation of Hopf bifurcating periodic solutions is investigated by using the global Hopf bifurcation theory of neutral equations. Finally, some numerical examples are carried out to support the main results.     

Extinction,periodicity and multistability in a Ricker model of stage-structured populations

We study the dynamics of a second-order difference equation that is derived from a planar Ricker model of two-stage (adult-juvenile) biological populations. We obtain sufficient conditions for global convergence to zero in the non-autonomous case yielding general conditions for extinction in the biological context. We also study the dynamics of an autonomous special case of the equation that generates multistable periodic and non-periodic orbits in the positive quadrant of the plane.     

Global asymptotic stability beyond 3/2 type stability for a logistic equation with piecewise constant arguments

In this paper, a logistic equation with multiple piecewise constant arguments is investigated in detail. We generalize the approach in two papers, [K. Uesugi, Y. Muroya, E. Ishiwata, On the global attractivity for a logistic equation with piecewise constant arguments, J. Math. Anal. Appl. 294 (2) (2004) 560-580] and [Y. Muroya, E. Ishiwata, N. Guglielmi, Global stability for nonlinear difference equations with variable coefficients, J. Math. Anal. Appl. 334 (1) (2007) 232-247], and establish a new condition for the global stability of the equation. Their results are given as one of the special cases. Moreover, we improve the 3/2 type stability condition under several dominance assumptions on the coefficients of the equation. Some examples and numerical simulations are also presented. All of these examples show that there are several conditions for the global stability of the equation, depending on the coefficients on the delay terms of the equation, beyond the 3/2 type stability condition.     

正负系数中立型差分方程的全局吸引性

A neutral difference equation with positive and negative coefficients△(xn-cnxn-k) pnxn-l-qnxn-r=0,n=0,1,2.…，is considered and a sufficient condition for the global attractivity of the zero solution of this equation is obtained, which improves and extends the all known results in the literature.