具有时滞的非自治N-种群Lotka-Volterra竞争系统的灭绝准则

研究了具有时滞的非自治 N-种群 Lotka-Volterra竞争系统 ,利用 Liapunov泛函改进了关于灭绝的准则     

A concrete example with multiple limit cycles for three dimensional Lotka–Volterra systems

The number of limit cycles for three dimensional Lotka–Volterra systems is an open problem. Recently, Yu et al. (2016) constructed some examples with the possibility of the existence of four limit cycles. Unfortunately, multiple limit cycles are not visible by numerical simulations, because all of them are very close to the interior equilibrium and extremely small. We present a concrete example with multiple limit cycles for three dimensional Lotka–Volterra systems which we can confirm them by numerical simulations. First we prepare the modified formula to compute coefficients of the normal form for the generalized Hopf bifurcation. Applying this formula to three dimensional Lotka–Volterra competitive systems with the aid of the computer algebra system, we derive the critical parameter values explicitly such that the interior equilibrium is exactly an unstable weak focus. Also we show that the heteroclinic cycle on the boundary of ${\mathbb{R}}_{+}^3$ is repelling. This implies that there exists a stable limit cycle by the Poincare–Bendixson theorem. Then, adding some suitable perturbations to parameters, we generate additional two limit cycles near the interior equilibrium by the generalized Hopf bifurcation. Finally we confirm that there exist three limit cycles by numerical simulations.     

制造商与两个具有竞争性的零售商的两阶段博弈模型

针对一个制造商和两个具有竞争性的零售商组成的供应链两阶段博弈模型.首先考虑下游零售商之间的Stackelberg博弈,然后又以整体最优讨论制造商为主导的Stackelberg博弈的两阶段博弈模型.数字实验结果表明:该策略不仅能提高制造商的利润,而且能改善销售商的利润,特别是对于供应链成员之间具有较高的竞争强度.     

工件可拒绝排序问题综述

可拒绝排序问题是兴起于2000年前后的有代表性、应用背景极强的的排序问题,是经典排序问题的衍生和推广.经典排序问题总是要求每个工件必须被加工,然而在实际中由于某些特殊原因,决策者会选择拒绝加工某些工件.把允许工件被拒绝的这类问题称为工件可拒绝排序问题,有的文献称之为外包的排序问题.这些问题不仅具有很强的应用价值,在理论上也有重要的意义.近年来该领域受到越来越广泛的关注,新的研究成果不断涌现.现就离线、在线情况下的可拒绝排序问题的进展情况作了全面介绍,展示了已有的研究成果和新的问题,给出了此方面的比较重要的参考文献,旨在帮助感兴趣的读者迅速了解问题研究的进展并由此进入此研究领域的前沿.     

高生长速度条件下的“层片↔棒状”共晶转变机理研究

低速生长条件下, 共晶“层片↔棒状”转变只由两相的体积分数控制. 高速情况下, 这种转变有时亦发生, 其转变机理不清楚. 本文应用竞争生长准则, 结合高速生长条件下层片共晶和棒状共晶生长模型研究了生长速度引起的“层片↔棒状”转变机理. 结果显示: 体积分数在临界值附近很小的范围内, 生长速度和溶质配分系数的增大可引起“棒状→ 层片”共晶转变; 而当体积分数远离临界值时, 转变不发生. 生长速度名义上引起“层片↔棒状”共晶转变实际上是由生长速度变化引起的体积分数的变化导致的. 关键词： “层片↔棒状”共晶转变 竞争生长 生长速度 体积分数     

多指标面板数据融合聚类分析

针对多指标面板数据的样品分类和历史时期划分问题,从多元统计分析理论角度提出一个多指标面板数据的融合聚类分析方法。该方法改进了多指标面板数据的因子分析和系统聚类方法,依据Fisher有序聚类理论,构造了Frobenius范数形式的离差平方和函数,提出了多指标面板数据的有序聚类方法。实证结果表明,该方法能够满足系统分析的统一性要求,保证指标之间的不相关;能够克服时间维度上均值处理造成的偏误,信息损失较少;能够解决面板数据有序聚类的问题;弥补了单一分析的片面性和局限性。     

A mathematical model of hotspot condensed phase ignition in the presence of a competitive endothermic reaction

We consider the propagation of a combustion front resulting from the gasless combustion of a condensed state fuel. The propagation of the front, essentially a premixed laminar flame, is supported by an exothermic reaction subject to possible heat loss through a competitive endothermic reaction. The dynamics of the endothermic process inducing the heat loss strongly depend on the temperature and the local fuel concentration. Through an analysis based on high activation energy, the steady-state values of the final burnt temperature as well as the burning velocity are obtained, and the control parameters are identified. Using a linear perturbation method, we assess the stability of the propagating front and obtain a condition for oscillatory behaviour. The critical parameter values for the transition from steady to oscillatory burning speeds are identified. The results represent a generalization of those obtained by Matkowsky and Sivashinsky to include the effects of heat loss induced by a competitive endothermic reaction.