ATTRACTORS OF NONAUTONOMOUS SCHRODINGER EQUATIONS

The long-time behaviour of a two-dimensional nonautonomous nonlinear SchrOdinger equation is considered. The existence of uniform attractor is proved and the up per bound of the uniform attractor' s Hausdorff dimension is given.     

耦合型Mathieu方程及其粒子的共振穿越

本文用多重尺度法讨论了耦合型Mathieu方程解的稳定性及其它的一阶不稳定区,并分析了粒子穿越v_x+2v_z=N共振线的动力学行为,导出了工程要求的最小加速电压。     

完全与不完全的随机网

本文证明了鞍点连线网在小扰动下可以产生完全随机网和不完全随机网两种情况,并按照动力系统理论讨论了两类随机网的结构.     

WAVELET APPROXIMATE INERTIAL MANIFOLD AND NUMERICAL SOLUTION OF BURGERS'''' EQUATION

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时空Chaos研究中的CML模型

通过对有关差分格式的稳定性分析，我们提出了一类新的格点耦合映射（ＣＭＬ）模型。数值试验表明：我们提出的ＣＭＬ模型是一类有效的研究时空复杂性的模型，特别是对于强耦合系统。     

An Approach to Analyse Phase Synchronization in Oscillator Networks with Weak Coupling

We study phase synchronization in oscillator networks through phase reduced method. The dynamics of networks is reduced to phase equations by this method. Analysing the phase equations through the master stability function method, one obtains that the oscillators with identical frequency can be in-phase synchronized by weak balanced coupling. Similarly, the problem of frequency synchronization of oscillators with different frequencies is transformed to the existence of a locally asymptotically stable equilibrium of the phase error system.     

非 Hamilton 系统的次谐分叉和马蹄

目前,浑沌理论引起了人们广泛的兴趣,已有一系列理论的结果.判断浑沌的发生通常是检验横截同宿点的存在.最近,严寅、钱敏证明了:对于异宿点,若具有横截 n-环,则同样存在 Smal 马蹄.对于二维的 Hamilton 系统受扰动后,Melnikov 给出了判定 Poincaré映射横截同宿点或异宿点存在的解析工具.本文讨论非 Hamilton 系统:=uv,(?)=1-u~2-v~2在适当的扰动下存在 Smal 马蹄,同时,用 Melnikov 方法讨论了次谐分叉及次谐分叉与马蹄的关系.     

半导体光磁电效应的非线性特征

本文从Shockley-Read统计出发,引入载流子寿命与浓度的相关性,将载流子的输运方程化为二阶非线性微分方程,并用双参数摄动法找到了方程的一般解,且在二级近似下,计算了半导体材料的短路电流和光导电流,揭示了大信号情况下光磁电效应的非线性特征,进一步拟合了实验数据。 关键词：     

SOME PHENOMENA FOR WEAK SPRING DUFFING EQUATION IN SUBHARMONIC AND ULTRASUBHARMONIC REGION

In this paper the situation in which weak spring Duffing equation gets into the chaos onaccount of small perturbation is discussed with Melnikov-Holmes′method,and somephenomena in which the different subharmonic and the ultrasubharmonic coexist with thechaos are discovered.