无穷维动力系统

今天的动力系统大致可分为微分动力系统、拓扑动力系统、无穷维动力系统、复动力系统、遍历论等方向。

Roughly speaking , dynamical systems consist of differential dynamical system , topological dynamical system , infinite dimensional dynamical system , complex dynamical system and ergodic theory etc.

基于完整的湿大气动力学方程组，利用无穷维动力系统的新理论和新方法，系统讨论了强迫耗散的非线性大气系统的定性理论及其应用。

Based on the complete dynamical equations of the moist atmospheric motion , the qualitative theory of nonlinear atmosphere with dissipation and external forcing and its applications are systematically discussed by new theories and methods on the infinite dimensional dynamical system .

利用了无穷维动力系统吸引集和吸引子概念以及挤压性质，证明了两个相同的二维Navier-Stokes方程在高频耦合条件下可达到完全同步化。

By using the concepts of absorbing sets , attractor and squeezing properties , the occurrence of complete synchronization of two high frequency coupled 2D Navier-Stokes equations is proved .

第四，通过先验估计，证明了广义Sine-Gordon方程在齐次边界条件和初始条件下所确定的无穷维动力系统在各种Sobolev空间的有界吸收集的存在性。

By the priori estimates , we prove the existence of absorbing set of the Sine-Gordon function under initial and the first bound condition in different sobolev space .

无穷维动力系统中惯性流形和吸引子

Inertial manifolds and attractors in infinite dimensional dynamical systems

无界域上无穷维动力系统解的长时间行为的研究

Long-time Behaviors for the Solutions of Infinite Dimensional Dissipative Dynamical Systems in Unbounded Domains

无穷维动力系统的近似惯性流形方法和多级有限元逼近

The Convergence for Approximate Inertial Manifold and Multilevel Finite Element in Infinite Dimensional Dynamics System

用无穷维动力系统的方法研究了一类流体超导系统的长时间行为。

The long time behaviour of the superconductivity liquids system has been studied by the Infinite dimensional dynamical systems method .

吸引子（包括全局吸引子，随机吸引子）是无穷维动力系统研究的中心内容之一。

Attractor ( includes global attractor , random attractor ) is that of central parts in studying infinite dimensional dynamical systems .

本文研究了数学物理中两类典型的具有耗散性的无穷维动力系统的渐近性理论。

In this paper , we study the asymptotic theory of two typical dissipative infinity dynamic systems in mathematics and physics .

理解动力系统的渐近行为是研究无穷维动力系统的主要内容，也是当代数学物理的重要问题之一。

The understanding of the asymptotic behavior of dynamical systems is one of the most important problems of modern mathematical physics .

为了研究状态为连续系统的动力学的复杂性，我们根据对无穷维动力系统讨论的结论，提出了一种新的映射模型。

A simple model based on the discussion for infinite dimensional system is introduced to investigate the dynamical complexity for continuous system .

大气和海洋动力学的理论研究的重要内容之一是考虑大气、海洋的无穷维动力系统。

One of the important contents in the dynamics is to study the infinite-dimensional dynamical systems of the atmosphere and the oceans .

运用具有两个参数的算子簇来描述非自治无穷维动力系统的方法，证明了该系统的一致吸引子的存在性。

Using the method of describing non-autonomous dynamical system by operator families with two parameters , we obtain the existence of their uniform attractor .

无穷维动力系统在非线性科学中占有极为重要的地位.格点系统是一类很重要的无穷维系统。

Infinite dimensional dynamical systems play an very important role in nonlinear science . Lattice systems are a kind of very important infinite dimensional dynamical systems .

在这种耗散型的无穷维动力系统中，吸引子的存在性是最重要的特征之一，系统的长时间性态完全被系统的吸引子所决定。

The existence of an attractor is one of the most important characteristics for a dissipative system , The long-time dynamics is completely determined by the attractor of the system .

利用无穷维动力系统的一致持续生存理论，得到该系统永久持续生存以及唯一正平衡点全局渐近稳定的充分条件，并分析了自食对此捕食系统稳定性的影响。

It is show that the system is uniformly persistent under some appropriate conditions , and sufficient conditions were obtained for the global stability of the positive equilibrium of the system .

对由一类非线性抛物型变分不等方程所描述的无穷维动力系统，给出了存在全局吸引子及弱近似惯性流形的充分条件。

The infinite dimensional dynamical systems governed by a class of nonlinear parabolic variational inequalities are considered . The sufficient conditions for existence of the global attractor and weakly approximate inertial manifold of the system are given .

无穷维动力系统中一类重要的问题是非线性扩散问题，它来源于自然界广泛存在的扩散现象，渗流理论、相变理论、生物化学以及生物群体动力学等领域都存在这种现象。

One of the important class of problems in nonlinear dynamics is the nonlinear diffusion problem . It comes from a variety of phenomena which exist widely in nature such as filtration , phase transition , biochemistry and dynamics of biological groups .

本文综述了无穷维动力系统近年来的发展概况，系统地介绍了它的理论基础以及有关结果，最后就无穷维动力系统发展趋势和意义作了一些讨论。

This paper reviews the development in studies of infinite dimensional dynamical systems in recent years , together with their basic theory and some results in relation with inertial manifold and attractor . A discussion is made on their development in future .

特别值得注意的是，将CNN中的有限个状态变量推广到无穷多个状态变量后，则得到一个无穷维的格点动力系统，其动力学行为变得非常复杂。

We should specially pay attention to the infinite-dimensions lattices dynamic system that we obtained when finite state quantities are changed to infinite in CNN and the dynamic behavior of the lattices dynamic system will be very complexity .