Bifurcation,several equilibria and multiple growth paths in the solow model with endogenous demographic transition

In this paper,the endogenous demographic transition function is integrated into the classical Solow model. It is proven that the differential equation which describes the model at least has a nonzero equilibrium. The differential equation has several equilibria when the technological level or the saving rate is not high enough and undergoes bifurcation at some specified parame-ter values. Therefore,the economy described by the model pre-sents multiple growth paths and "Malthusian Poverty Trap" when the technological level or the saving rate is low.     

一类非线性色散 BBM 方程的尖角子解

利用动力系统分岔方法结合常微分方程的渐近分析证明了 B（2，2）方程尖角子解的存在性，并给出了这些解的解析表达式。数值模拟进一步验证了所得结果的正确性。     

Quasi-periodicity in the autonomous glycolytic system

This study predicts that quasi-periodic oscillations could exist in a detailed model of glycolysis that is analyzed in an autonomous system. In addition to period-doubling, quasi-periodic and period-adding bifurcation, a new stationary branch, which lies in between the thermodynamic and flow branches, is also uncovered in the glycolytic reaction system. Results presented in this study illustrate that the Michaelis constant （K4GAP） of glyceraldehyde 3-phosphate dehydrogenase for glyceraldehyde 3-phosphate has great influences on glycolytic oscillations, in which increasing K4GAP widens the range of flow rate over which quasi-periodic oscillations exist.     

具有抛物线和双曲线解的三次系统极限环的存在性

研究具有抛物线和双曲线解的平面三闪微分系统（Ｅ）３的极限环存在性问题，得到具有以任意两条不相交的抛物线ψ（ｘ，ｙ）＝０和双曲线Ｆ（ｘ，ｙ）＝０为解的三次系统（Ｅ３）在全平面不存在极限环的结果，当 线解相切时可得具有相切的二曲线解ψ（ｘ，ｙ）＝０与Ｆ（ｘ，ｙ）＝０的一类三次系统，利用Ｈｏｐｆ分枝定量可得，在奇点Ｏ（０，０）的邻域内存在的唯一的不稳定极奶环Гλ，且当λ－０时，Гλ收缩于奇点Ｏ。     

坐标变换的不变量

本文证明了两个非常重要的同宿分支量，发散量积分和Ｍｅｌｎｉｋｏｖ向量，均为Ｃ＾２坐标变换的不变量，从而它们均为系统的内蕴量。     

两参数对称音叉式分岐问题的计算

对两参数对称音叉式分岐问题,构造了扩张系统,证明了辅助方程的正则性,并给出牛顿法实现的数值例子。     

LOCAL STABILITY AND BIFURCATION IN A THREE—UNIT DELAYED NEURAL NETWORK

A system of three-unit networks with coupled cells is investigated.The general formula for bifurcation direction of Hopf bifurcation is calculated and the estimate formula of period of the periodic solution is given.     

顶点融合范畴的Z2-扩张及应用

利用非可逆单对象与其对偶的张量积分解,研究了顶点融合范畴的Z₂-扩张。 然后给出此类融合范畴的泛分次结构,并讨论了它在半单Hopf代数分类中的应用。     

自相食对种群的调节效应

通过引用的组建一些简单的年龄结构种群模型，利用微分方程线性稳定性理论和生物种群动力系统的分岔理论分析这些模型的平衡态的局部线性稳定性，并借助数值模拟的方法讨论这些模型动太性质的差异，对不同模型的比较说明自相食对种群的稳定状态有重要的影响。