充分条件

We obtain some sufficient conditions of uniformly continuous function.

得到了函数一致连续的几个充分条件。

As an application, it is proved that a continuous map of an interval is chaotic iff it is distributively chaotic in a sequence.

给出紧度量空间上连续映射按序列分布混沌的一个充分条件，并证明区间连续自映射是混沌的当且仅当它是按某序列分布混沌的。

In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.

第一章讨论了一类具脉冲时滞微分方程周期正解的存在性，通过建立锥上的全连续算子，利用Krasnoselskii不动点定理，得到了存在周期正解的若干充分条件。

By using the method of an abstract continuous theorem of k-set contractive operator and some analysis technique. Sufficient conditions are derived for the existence of at least one strictly positive periodic solution of periodic two-species Lotka-Volterra competition dynamics systems with neutral delay and several deviating arguments.

利用k-集压缩算子抽象连续理论和某些分析技术，导出了此具有中立时滞和变差元的周期两种群Lotka-Volterra竞争动力系统至少存在一个严格正的周期解的充分条件。

We give the sufficient-necessary condition of convergence and the sufficient condition of eventually contractive convergence introduced by Fisher is explained.

另一方面，根据线性控制理论的某些结果，提出了用系统的特征值来分析解码吸引子的收敛性的新手段；并给出了收敛的充要条件以及Fisher终值压缩收敛的充分条件。

Convergence, convergence in probability, and convergence in distribution. And some sufficient and/or necessary conditions are also given.

收敛、统计依概率收敛的充要条件或充分条件，此外还讨论了几种收敛性之间的一些关系。

By analysis of such models, a method, which is used to find out the region of convergence and to study the local stability for strong nonlinear system, are derived. Thus, we can consider the strong nonlinear neural networks using such method.

利用新的比较方法，考虑了具变时滞和常恢复率的同质人群HIV梯度传染病模型，得到了一个阈值，当阈值小于1时，疾病消除平衡点全局指数渐近稳定，当阈值大于1时，传染病平衡点存在唯一，同时得到该传染病平衡点局部指数渐近稳定的充分条件。

A fixed point of a discrete-time neural network with generalized input-output function and by using the converse theorem of Lyapunov function we study the uniformly asymptotical stability of equilibrium in this discrete-time neural network with variable weight and give some sufficient conditions that guarantee the stability of it.

本文首先介绍了几类离散神经网络模型的由来及其研究概况，利用Schauder不动点原理证明了一类具有广义输入输出函数的离散神经网络模型平衡点的存在性，利用Lyapunov函数逆定理给出了这类离散神经网络模型在时变权值下的一致渐近稳定性的充分条件。

In this thesis, we firstly introduce several class of discrete-time neural network models and the research progress of the neural networks. By Schauder fixed-point principle we prove the existence of an equilibrium (i.e. a fixed point) of a discrete-time neural network with generalized input-output function and by using the converse theorem of Lyapunov function we study the uniformly asymptotical stability of equilibrium in this discrete-time neural network with variable weight and give some sufficient conditions that guarantee the stability of it.

本文首先介绍了几类离散神经网络模型的由来及其研究概况，利用Schauder不动点原理证明了一类具有广义输入输出函数的离散神经网络模型平衡点的存在性，利用Lyapunov函数逆定理给出了这类离散神经网络模型在时变权值下的一致渐近稳定性的充分条件。

Using the convex cone theory of nonlinear functional analysis, thesufficient condition is obtained in which the system has at least two non-trival w-periodicsolutions.

点定理讨论了n维非自治系统，给出了该系统存在两个非零周期解的充分条件。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。