连续动力系统

In Chapter 1, a brief reviews of bifurcation theories and chaos theory for flows and maps are presented.

第一章是关于动力系统的局部分支与混沌的预备知识。简要地介绍连续动力系统和离散动力系统的各种局部分支理论，同时对混沌的一些定义、特征及相关的判别方法也给出简要的介绍。

It takesthe weighted average of the L2 norm of the difference of the observation and thesolution of the system and the L2 norm of the difference of conormal derivativeat the different sides of the interface for every subdomain as cost functional andthe smooth coefficients of the subproblem and the value of solution of the originalproblem at interface as identification parameters;Using the property of continu-ous functional defined on compact set,the existence of the optimal solution of theidentification problem is proved;The necessary conditions of optimality charac-terized by the system equation,the adjoit equation and the variational inequalitysimultaneously are given by introducing the conception ofdifferential andadjoit variable;An algorithm is devised and its flow graph is given.

其次，针对分片光滑动力系统的特征，结合正演过程的区域分解算法，建立了分片光滑系统的分解区域参数辨识模型，该模型以子区域上解的实测值与计算值之差的L2范数和界面两侧的通量差的L2范数的加权平均作目标泛函，各子问题的光滑系数及界面上真解的值为待辨识参量；利用紧致集上连续泛函的性质，证明了子区域上参数辨识问题最优辨识参量的存在性；引入微分的概念，借助伴随变量，给出了由系统方程，伴随方程和变分不等式共同表征的最优性必要条件；根据此必要条件设计了算法，给出了算法的程序框图。

About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system.

关于一本书的第三个重点是存在和关于离散或连续动力系统全局吸引流动性。

By using the theories and methods of impulsive,discrete and continuous dynamical system,arithmetic operators,optimiza-tion and numerical simulation,we study locally and globally asymptotieal stability of the boundary periodic solutions,and the permanence of the these systems.

以脉冲动力系统理论为基础，同时结合离散动力系统、连续动力系统、算子理论、优化理论等相关的理论和方法，在已有的研究成果的基础上，研究这些模型的边界周期解的局部和全局渐进稳定性、系统的持续生存、周期解的存在性与唯一性以及周期解的轨道稳定性等等。

Conley index; prime isolated invariant set; bifurcation point; discontinuity dynamical systems; finite piecewise continuous map; coding; rigorous computer assisted proof; chaos; Ikeda map

基础科学，数学，动力系统理论Conley指标；素孤立不变集；分支点；间断动力系统；有限分片连续映射；编码；计算机严格辅助证明；混沌； Ikeda映射

In this paper, the limit cycles in a nonlinear deterministic model in the continuous culture vessel with variable yield is studied.

用微分动力系统的定性理论研究了一个非线性连续微生物培养动力系统的极限环问题，探讨和估计了存在极限环的条件和极限环的周长。

In mathematical viewpoint, this kind of systems are called non-smooth dynamical systems, i.e., right-hand sides of the systems are not continuous or differentiable.

从数学的观点来看，这一类系统称为非光滑动力系统，即这些系统的右端是不连续或不可微的。

Many problems of dynamical systems can be reduced to an iterative functional equation or an iterative functional differential equation.

根据系统变化的规律可分为由微分方程描述的连续动力系统和由映射迭代揭示的离散动力系统。

In the third chapter, we construct a neural network of continuous-time dynamical system to investigate a nonlinear equation.

在第三章，我们利用连续动力系统神经网络来讨论非线性方程的求解问题。

In recent years, the researches in mathematical biology which modeled by normal differential equations are mainly concentrated on two branches: 1 continuous biological dynamical systems; 2 impulsive semi-dynamical systems.

生物数学中以生物动力系统为基础的研究近年来得到了长足的发展，其中以微分方程为模型的研究工作主要集中在连续动力系统和脉冲动力系统上。

On closer examination, though, this is not a vote for multilateralism but just the opposite.

仔细审视后我们发现，这并非是对多边主义投出的赞成票，而是恰好相反。

Uncovering their weak spots, so I can defeat them.

揭露出他们的弱点，这样我就可以打败他们了。