三阶泛函微分方程的周期解的存在性

本文利用重合度理论研究了一类三阶泛函微分方程方程的2π-周期解的问题,获得了该方程存在2π-周期解的若干新结论,改进推广了有关文献中的已有结果．     

受迫广义KdV-Burgers方程行波解的存在唯一性

本文研究具有受迫性的广义二维KdV-Burgers方程的周期行波解,为了获得周期行波解的存在唯一性定理,使唤用特定系数法和Schauder不动点定理获得了受迫广义KdV-Burgers方程周期行波解存在唯一性的条件.并获得了周期行波解的一些先验估计式.     

Lotka-Volterra型N-种群竞争系统的持久性和稳定性

本文研究一类具有无穷时滞的概周期Lotka-Volterra型N-种群竞争系统的持久性和全局渐近稳定性.一些新的充分条件被得到.     

Duffing方程的唯三周期解问题

考虑Duffing方程x+g(x,t)=h(t),在g(x,t)满足简单的凸凹性条件。以及g＇(x,t)跨越第一共振点时,本文指出,当强迫振动项h(t)充分小时,所讨论的Duffing方程的2π周期解恰有三个.     

二次概周期系数微分方程的概周期解

利用指数二分性,Schauder不动点定理和Grownwall不等式证明了一类概周期系数微分方程的概周期解、有界解的存在唯一性及概周期解的全局吸引性.     

OPTIMAL HARVESTING POLICY FOR INSHORE-OFFSHORE FISHERY MODEL WITH IMPULSIVE DIFFUSION

This article studies the inshore-offshore fishery model with impulsive diffusion. The existence and global asymptotic stability of both the trivial periodic solution and the positive periodic solution are obtained. The complexity of this system is also analyzed. Moreover, the optimal harvesting policy are given for the inshore subpopulation, which includes the maximum sustainable yield and the corresponding harvesting effort.     

微分算子扰动问题的值域研究

本文研究作用在C2周期函数空间上的微分算子u→u″ g(u) ,其中g(u)为连续有界函数.我们将证明上述微分算子的值域限制在周期函数空间的“超曲面”中.     

Banach空间二阶周期边值问题解的存在性

利用一些比较结果，讨论了Banach空间中二阶周期边值问题解的存在性，获得了若干解的存在性与唯一性结果。     

具有时滞的非自治的捕食-食饵系统的全局吸引

考虑一个具有离散时滞的非自治的捕食—食饵系统。系统是由3种群组成的，其中一个为捕食者，另两个为食饵种群。本文的目的是给出时滞对系统的持续生存是无害的，从而确定了系统的周期解全局吸引的条件。     

Nonlinear Correlations of Protein Sequences and Symmetries of Their Structures

We investigate the nonlinear correlations of protein sequences by using the nonlinear prediction method developed in nonlinear dynamical theory. It is found that a lot of protein sequences show strong nonlinear correlations and have deterministic structures. Further investigations show that the strong nonlinear correlations of these protein sequences are due to the symmetries of their tertiary structures. Furthermore, the correlation lengths of the sequences are related to the degrees of the symmetries. These results support the duplication mechanism of protein evolution and also reveal one aspect how amino acid sequences encode their spatial structures.