一个具有两个吸引子的偏微分方程组

本文构造了一个具有两个吸引子的反应扩散方程组，并讨论了吸引子的结构。     

An example of PDE with two attractors

ＡＮＥＸＡＭＰＬＥＯＦＰＤＥＷＩＴＨＴＷＯＡＴＴＲＡＣＴＯＲＳＷａｎｇＧｕａｎｘｉａｎｇ（王冠香）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＳｕｚｈｏｕＵｎｉｖｅｒｓｉｔｙ,Ｓｕｚｈｏｕ２１５００６Ｐ．Ｒ．Ｃｈｉｎａ）ＸｕＺｈｅｎｙｕａｎ（徐...     

带三次多项式的反应扩散方程吸引子维数分析

详细分析了以三次多项式作为非线性项的反应扩散方程在荻氏边界条件下整体吸引子Ｈａｕｓｄｏｒｆｆ维数随各参数的变化情况，给出了存在零维吸引子的条件。     

关于Kuramoto-Sivashinsky方程的吸收集半径

给出了Kuramoto-Sivashinsky方程吸收集半径的优化估计。证明了,当粘性系数趋向某临界值时,吸收集半径将趋于零。这与已有结果比更符合物理直观。     

Stability analysis of delayed cellular neural networks with and without noise perturbation

The stability of a class of delayed cellular neural networks (DCNN) with or without noise perturbation is studied.After presenting a simple and easily checkable condition for the global exponential stability of a deterministic system,we further investigate the case with noise perturbation.When DCNN is perturbed by external noise,the system is globally stable.An important fact is that,when the system is perturbed by internal noise,it is globally exponentially stable only if the total noise strength is within a certain bound.This is significant since the stochastic resonance phenomena have been found to exist in many nonlinear systems.     

On radii of absorbing sets for Kuramoto-Sivashinsky equation

１ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄｔｈｅＭａｉｎＴｈｅｏｒｅｍＩｔｉｓｋｎｏｗｎｔｈａｔｔｈｅｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄｉｓａｐｏｗｅｒｆｕｌｔｏｌｆｏｒｒｅｄｕｃｉｎｇａｎｉｎｆｉｎｉｔｅ＿ｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｔ...     

Improved Estimate on Dimension of Inertial Manifold for Kuramoto-Sivashinsky Equation

Ｉｔｉｓｋｎｏｗｎｔｈａｔｔｈｅｉｎｅｒｔｉａｌｍａｎｉｆｏｌｄｉｓａｐｏｗｅｒｆｕｌｔｏｏｌｆｏｒｒｅｄｕｃｉｎｇａｎｉｎｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌｄｙｎａｍｉｃａｌｓｙｓｔｅｍｔｏａｆｉｎｉｔｅｄｉｍｅｎｓｉｏｎａｌｏｎｅ．Ｈｏｗｅｖ...     

有噪及无噪的时滞细胞神经网络稳定性分析

分析了一类时滞细胞神经网络(DCNN)系统在无噪声和有噪声干扰情况下的稳定性．首先针对确定性系统给出了一种简单且容易验证的全局指数稳定性条件,然后讨论了噪声干扰下系统的稳定性．当DCNN被外部噪声扰动时,系统是全局稳定的．重要的是,当系统被内在噪声扰动时,只要噪声总强度控制在一定范围内,系统是全局指数稳定的．鉴于随机共振现象在越来越多的非线性生物系统中被发现,这种稳定性具有重要意义．     

Explicit Dimensional Formula of Atractor for Damped Sine-Gordon Equation with Neumann or Periodic Boundary Conditions

ＥｘｐｌｉｃｉｔＤｉｍｅｎｓｉｏｎａｌＦｏｒｍｕｌａｏｆＡｔｒａｃｔｏｒｆｏｒＤａｍｐｅｄＳｉｎｅＧｏｒｄｏｎＥｑｕａｔｉｏｎｗｉｔｈＮｅｕｍａｎｎｏｒＰｅｒｉｏｄｉｃＢｏｕｎｄａｒｙＣｏｎｄｉｔｉｏｎｓＷａｎｇＧｕａｎｘｉａｎｇ（王冠香）ＺｈｕＳ...     

Kuramoto-Sivashinsky方程的渐近吸引子

本文给出了一周期边界条件下Ｋ－Ｓ方程的有限维渐进吸引子（Ａｓｙｍｐｔｏｔｉｃ Ａｔｔｒａｃｔｏｒ）而非通常的近似吸引子（Ａｐｐｒｏｘｉｍａｔｅ Ａｔｔｒａｃｔｏｒ）。