查询词典 periodic function

With the help of comparison theorem, sufficient conditions which guarantee permanence of the system are obtained. For the almost periodic case, by constructing a suitable Liapunov function, we obtained that the system has a unique globally asymptotically stable positive almost periodic solution. Finally, we study a multispecies predator-prey system with stage structure and Holling II type functional response.

第二部分考虑具有阶段结构的非自治扩散捕食系统，利用比较定理得到该系统持久生存的充分条件，其后在概周期情形下通过构造合适的Liapunov函数得到了保证该系统存在唯一一个全局渐近稳定的概周期解的条件。

Double homoclinic loops; Resonant eigenvalues; Nontwist; Periodic orbit; Bifurcation; Periodic solution; Predator-prey system; Fixed point theorem; Coincidence degree; Delay; Functional response function

基础科学，数学，动力系统理论双同宿环；共振特征根；非扭曲；周期轨；分支；周期解；捕食者-食饵系统；不动点定理；重合度；时滞；功能反应函数

PartⅡ,Applying the developed and extended direct algebraic methods that presented in recent years and based on the 2+1 dimensional variable separation solutions,abundant Jacobi elliptic function doubly periodic waves and periodic propagating wave patterns for many 2+1 dimensional nonlinear wave models are obtained,and in long wave limit solitary waves are derived as well.

第二部分，本文拓展和推广(来源：a2AB7aC论文网www.abclunwen.com)了新近发展的几种典型的直接代数方法和基于分离变量解的间接方法，获得多个2+1维非线性波动模型丰富的雅克比椭圆函数双周期波解和周期传播波模式，并得到长波极限情形下存在的非线性孤立波。

Firstly, we consider SIQR epidemical models with continuous and pulse vaccinations; the reproduction numbers have been obtained for those models; by using Dulac function, we prove the global stabilities of equilibrium of SIQR model with continuous vaccination. In the SIQR epidemical models with pulse vaccinations, we have also discussed the existence of the infection-free periodic solution, the global stabilities of the infection-free periodic solutions, and the effectiveness of pulse vaccination and continuous vaccination policies has been compared for the two models.

文中首先考虑具有连续免疫接种和脉冲免疫接种的SIQR传染病模型，分别获得了它们各自的基本再生数；利用Dulac函数方法证明了具有连续免疫接种的SIQR模型无病平衡点的全局渐近稳定性；在脉冲免疫接种下SIQR传染病模型里，讨论了无病周期解的存在性，证明了该周期解的全局渐近稳定性，并且对连续和脉冲接种下的SIQR传染病模型的接种效率进行了比较。

Nonlinear flexural wave equation is solved by the Jacobi elliptic function expansion method. Two kinds of exact periodic solutions of the nonlinear equations are obtained, that is, the shock wave solution and the solitary wave solution. The necessary condition for existence of exact periodic solutions, shock solution and solitary solution is discussed, which is consistent with the qualitative analysis.

利用Jacobi椭圆函数展开法，对该非线性方程进行求解，得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解，讨论了这些解存在的必要条件，这与定性分析的结果完全相同。

Using algebraic methods which include extended Tanh-method,some new solitary solutions to the DBM and Log-DBM equation,such as singular solitary solutions,double singular peakon solitary wave solutions,double solitary wave solution with peakon and singular periodic solitary wave solutions are obtained..With the aid of an auxilitary function combined with the elliptic integral of the first kind,periodic solitary solution,singular and periodic singular solitary solutions can be obtained.

第三章利用扩展的Jacobi椭圆函数展开法研究了方程，并给出ZK-MEW方程的Jacobi椭圆函数解，特别的，当模数m→0和m→1时，其中一部分解退化为三角函数解和孤立波解；其次使用sn-cn拟设法，研究了K(k，s，1)方程，得到了k=s=3时的新的精确解，并在模数m→0和m→1时得到了丰富的三角函数和孤立波解。

By virtue of the invariant manifolds and conservative property of Hamiltonian system, we construct a"switching algorithm"to compute the periodic solution of equation (4) when the dispersion distribution σ is periodic and piecewise constant function.

4运用不变流形的分析方法和哈氏系统的守恒性质，给出了当色散分布σ为周期的分片常数情形计算方程(4)的周期轨的一个"开关算法"。

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论，并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法，其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法，最后，介绍了两类数值求解非线性微分方程问题的方法。

This system is permanent by comparative principle and globally asymptotically stable through constructing a Liapunov function; for the periodic case, the research has obtained conditions for existence, uniqueness and stability of a positive periodic solution.

利用比较原理研究了系统的持久性，通过构造Liapunov函数证明了系统的全局渐近稳定性，在假设系统为周期系统的条件下得到了正周期解的存在唯一性和全局渐近稳定的充分条件。

Furthermore, when the system is a periodic system, sufficient conditions are obtained that guarantee the existence, uniqueness and global attractivity of the positive periodic solution by applying the Brouwer fixed theorem and the method of constructing Liapunov function.

利用比较原理给出了系统一致持久性的充分条件；当系统是周期系统时，应用Brouwer不动点原理和构造Liapunov函数的方法给出其存在惟一且全局吸引的ω-周期正解的充分条件，并通过实例验证了文中定理条件的可实现性。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了