多滞量的反应扩散方程的分支环（Ⅱ）—分支环的存在性定理

一文研究一类定义在单位圆周上带有两个滞量的纯量反应扩散方程，继续文[９]的讨论，并借助于文[２]中的Ｂｉｒｋｈｏｆｆ规范型理论，给出了二维不变环的存在性结果。     

非线性反应-扩散方程指数吸引子的存在性

证明一类非线性反应-扩散方程指数吸引子的存在性。为此,证明对应的解半群是Lipschitz的,且对应的离散半群满足squeezing特性。     

Existence of Periodic Solutions for Reaction-diffusion Systems with Time Delays

Periodic solutions of reaction-diffusion systems with time delays are investigated. The upper and lower control function of nonmonotone reaction term is constructed. It is showed that the function satisfies a global Lipschitz condition and quasimonotone. A sort of effective method of studying differential equation with nonmonotone reaction term is gained. It is shown that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled to-upper and lower solutions.     

随机反应扩散神经网络的鲁棒稳定性

研究一类具有分布时滞和反应扩散的随机细胞神经网络,通过构造Lyapunov泛函,并利用It公式以及线性矩阵不等式（LMI）,得到不确定系统鲁棒稳定的充分条件.     

一类奇异线性反应扩散方程组的解

运用有界线性算子半群,把一类奇异线性反应扩散方程组用积分方程组表示出来,运用Gronwall不等式、迭代法、不等式的放缩法研究这类奇异线性反应扩散方程组,得到其解.     

不动点技巧在反应扩散模糊随机周期时滞系统稳定性分析中的应用

利用不动点定理、变分方法、线性矩阵不等式技巧、李雅普诺夫方法和Banach压缩映射原理,给出了线性矩阵不等式条件的反应扩散马尔科夫跳跃周期模糊时滞系统的随机稳定性判据,并通过建立在乘积空间上的压缩映射克服了反应扩散模型带来的数学上的困难.最后,利用数值实例证实了所述方法的有效性.     

Existence and Stability of Periodic Solutions for Reaction-diffusion Systems with Time Delays

Periodic solutions of reaction-diffusion systems with time delays are investigated. It is constructed that the - per and lower control function of nonmonotone reaction term, and it is showed that the function satisfies a global Lipschitz condition and quasimonotone. A sort of effective method of studying differential equation with nonmonotone reaction term is gained. By using the method of upper and lower solutions and fixed point theorem, it is shown that periodic solutions of this system exist when reaction-term is not monotone and the boundary value system has a pair of coupled-upper and lower solutions. Some methods for proving the stability of the periodic solution are also given. And some known resuits are extended.