一类非线性差分方程的持久性与全局吸引性

本文研究了差分方程ｘ（ｎ＋１）＝ｘｐｎｆ（ｘｎ，ｘ（ｎ－ｋ１），…，ｘ（ｎ－ｋｒ））的持久性与全局吸引性，解决了文［３］提出的两个研究课题，所得结果包含了文［３］的相应结果．     

非线性时滞差分方程的全局吸引性

得到了具有多重时滞非线性差分方程x(n 1)-x(n) ∑i=1^k pi(n)fi(x(gi(n)))=0,n=0,1,2,…的每个解趋于零的充分条件。     

一类非线性时滞差分方程的全局吸引性

研究非线性时滞差分方程△xn anxn f(n,0√s=-k^-qs,nxs n）＝0，给出保证方程每一解{xn}趋于0的一族充分条件，推广并改进了已有的结果。     

一类时滞差分方程的全局吸引性

本文得到一类时滞差分方程解的全局吸引性的几个新的充分条件，包含或改进了一些已知结果，把G.Ladas的一个猜想的研究向前推进了。     

一类时滞差分方程的全局吸引性及其应用

研究一类广泛的时滞差分方程的全局吸引性 ,在较弱的前提下给出其零解全局吸引的充分条件 .将定理应用于红血球增长差分模型及广义 L ogistic差分模型 ,所得定理推广和改进了已有的结果     

一类差分方程的全局吸引性

考虑非自治差分方程xn 1=xnexp(rn 1-xn/1 λxn),n∈N的全局吸引性．这里{rn}是非负实数列，λ≥0，我们获得了方程每一解在初始条件下趋于1的充分条件．     

高阶非线性差分方程的全局吸引性

研究了差分方程 xn 1 =a - bxn- k A - xn( a≥ 0 ,A≥ b≥ 0 )的全局稳定性和正解的周期性质 .证明了方程的一个正平衡点是一个全局吸引子 ,并给出了相应的吸引域     

二阶非线性差分方程的全局吸引性

[摘　要] 研究了差分方程xn+1=a-bxn-1A-xn(a≥0,A≥b≥0)的全局稳定性和正解的周期性.证明了方程的一个正平衡点是一个全局吸引子,并给出了相应的吸引域.     

一类三阶有理差分方程的全局吸引性

本文主要讨论一类三阶有理差分方程x_(n 1)=α βx_n/A Bx_n Cx_(n-1) Dx_(n-2),n=0,1,0…其中α,β,A,B,C,D∈(0,∞),初始值x-2,x-1∈[0,∞),x0∈(0,∞)的全局吸引性,从而推广文[1]的结论。     

具有时滞和阶段结构的捕食系统的持久性和全局吸引性

研究一类具有时滞和阶段结构的捕食系统.利用微分方程的比较原理和通过构造适当的Lyaponov泛函,得到保证此系统持久性和全局吸引性的充分条件.最后举例说明结论的可行性并且讨论了所得结果的生态意义.     

Delay‐dependent criteria on the global attractivity of Nicholson's blowflies model with patch structure

In this paper, we investigate the effect of delay on the asymptotic behavior of Nicholson's blowflies model with patch structure and multiple time‐varying delays. By using the fluctuation lemma and some differential inequality technique, delay‐dependent criteria are obtained for the global attractivity of the addressed system. Meanwhile, some numerical examples are given to illustrate the feasibility of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

带有Holling IV功能反应的离散半比率依赖捕食-食饵系统的持久性和全局吸引性

In this paper, we investigate a discrete semi-ratio dependent predator-prey system with Holling IV type functional response. For general nonautonomous case, sufficient conditions which ensure the permanence and the global stability of the system are obtained. Meanwhile, we discuss the existence of the positive periodic solution and global stability of the system.     

Global attractivity in nicholson's blowflies

We established sufficient conditions for the global attractivity of the positive equilibrium of the delay differential equation [Ndot](t) ≡ ?δN(t) + PN(t–τ)e^?aN(t–τ) which was used by Gurney, Blythe and Nisbet [1] in describing the dynamics of Nicholson's blowflies     

Dependence of stability of Nicholson's blowflies equation with maturation stage on parameters

The stability of Nicholson''s blowflies equation with maturation stage is investigated by reducing the number of parameters in the original model. We derive the condition on the stability of the positive equilibrium of the model, and discuss the dependence of the stability on the parameters by analyzing geometrically the dependence of real parts of eigenvalues of the characteristic equation with fewer parameters on the parameters. By restoring parameters, the condition on the stability of the positive equilibrium of the original model are formulated explicitly, and the corresponding regions are depicted for some different cases. The obtained result shows that the parameter determining the maximum reproductive success of the population affects only the size of the positive equilibrium, but plays no role in determining its stability.     

一类时滞差分方程平衡点的全局吸收性

考虑时滞差分方程xn 1-xn=rnxn1-xn-kn/1-λxn-kn,n=0,1,2…,其中|rn|是非负实数例,{kn}是正整数列,{n-kn}非单调递减,且limn→∞（n-kn）=∞,λ∈0[0,1）,获得了保证方程每一正解趋于正平衡点的充分条件,改进和推广了[6,7]等已有的结果。     

Permanence and global attractivity for facultative mutualism system with delay

In this paper, we consider a facultative mutualism system with different delays. Sufficient criteria for permanence and global attractivity for the system are established. Ultimate uniform boundedness of the solutions ensures permanence. For the global attractivity of the system, magnitude of the delays plays a major role. Copyright © 2003 John Wiley & Sons, Ltd.     

Bifurcation analysis on a discrete model of Nicholson's blowflies

In this paper, the discrete Nicholson's blowflies model with delay is considered. First, the stability of the equilibria of the system is investigated by analyzing the characteristic equation and then the existence of fold and Neimark–Sacker bifurcations are verified. Subsequent to that, the direction and stability of the bifurcation are determined by using the normal form theory and center manifold theorem. Finally, some numerical simulations are carried out in order to support the results of mathematical analysis.     

Global exponential convergence in a delayed almost periodic Nicholson's blowflies model with discontinuous harvesting

This paper is concerned with a delayed Nicholson's blowflies model with discontinuous harvesting, which is described by an almost periodic nonsmooth dynamical system. Under some reasonable assumptions on the discontinuous harvesting function, by using the Filippov regulation techniques and the theory of dichotomy, together with the Halanay inequality, we establish some new criteria on the existence of positive almost periodic solution and its convergence. An example with numerical simulation is also presented to support the theoretical results.     

平方非线性Lotka-Volterra型时滞人口生长模型平衡点的全局吸引性

考虑平方非线性Lotka-Volterra型时滞人口模型 N(t)=N(t)[a+bN(t-T)-cN~2(t-t)](1) 我们获得了(1)唯一非负平衡点全局吸引的充分条件,改进了Gopalsamy、Ladas和Kuang中相应结论.     

具时滞离散互惠系统的持久性

研究具有无穷时滞离散互惠系统,得到保证系统持久性的一组充分条件．