Stabilization of stochastic complex networks with delays based on completely aperiodically intermittent control

This paper investigates the stabilization problem of stochastic complex networks with delays via completely aperiodically intermittent control. Superior to most existing results based on aperiodically intermittent control strategy that can only satisfy quasi periodicity, our proposed control scheme can render the lower bound of certain control intervals to be arbitrarily small, the upper bound of certain control periods to be very large and the proportion of rest intervals to be any value in (0,1). Thus, the constraints are loosened and the conservativeness is reduced compared with the existing related results. This is accomplished by presenting novel concepts, that is, average control rate and average control period. Under the designed controller, the studied networks are stable with small time delays and large time delays, respectively. Finally, the simulation results are provided to verify the effectiveness of the proposed control scheme.     

Stage-structured Harvest Models

We formulate a stage-structured population model where the population is divided to two classes, the juveniles and the adults. Then, we include harvest in the model and assume that the harvesting is only on adults. The cases where the harvesting rate is constant, proportional to the amount of adults, or of Holling-II type are studied. While the model dynamics are relatively simple when the harvesting rate is proportional, the model system with a constant or a Holling-II type harvesting rate can have multiple positive equilibria. We explore the existence of all possible equilibria and investigate their stability. We also give numerical examples to confirm our findings.     

连串反应中控制火焰的耦合GKS-CGL方程组解的极限行为

本文考虑连串反应中控制火焰的耦合广义Kuramoto Sivashinsky-Ginzburg Landau(GKS-CGL)方程组的周期初值问题,主要研究其解在系数g→0和δ→0时的极限行为.首先,采用Galerkin方法,通过构造一系列精细的先验估计,得到GKS-CGL方程组周期初值问题整体光滑解的存在唯一性.其次,利用一致有界估计证得GKS-CGL方程组极限解收敛,并给出解的收敛率估计.     

A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels

In this work, we propose a Jacobi-collocation method to solve the second kind linear Fredholm integral equations with weakly singular kernels. Particularly, we consider the case when the underlying solutions are sufficiently smooth. In this case, the proposed method leads to a fully discrete linear system. We show that the fully discrete integral operator is stable in both infinite and weighted square norms. Furthermore, we establish that the approximate solution arrives at an optimal convergence order under the two norms. Finally, we give some numerical examples, which confirm the theoretical prediction of the exponential rate of convergence.     

基于一阶Takagi-Sugeno系统的Pi-Sigma网络的改进神经-模糊梯度学习算法

This paper presents a Pi-Sigma network to identify first-order Tagaki-Sugeno（T-S） fuzzy inference system and proposes a simplified gradient-based neuro-fuzzy learning algorithm.A comprehensive study on the weak and strong convergence for the learning method is made,which indicates that the sequence of error function goes to a fixed value,and the gradient of the error function goes to zero,respectively.     

一类具有非线性发生率和治疗函数的传染病模型研究

传染病动力学系统的数学建模中,合理的使用非线性发生率往往更能使模型与实际相吻合.并且在实际的疾病防治过程中,由于受到空间人力物力资源的影响一般存在最大治疗容量的限制.结合这两种情况建立了一类含非线性发生率和最大治疗容量限制的传染病模型.通过分析这个模型,得到无病平衡点和正平衡点的存在性、稳定性.进一步取发生率和治疗系统达到最大容量时的感染者人数作为分支参数,得到了Hopf分支和Bogdanov-Takens分支的存在条件,并进行了数值模拟.     

常利率复合二项双险种风险模型的研究

提出了含利率因素的复合二项双险种风险模型,并在有关假设的基础上,给出了此模型下保险公司稳定经营的必要条件;证明了索赔时刻的盈余过程是一马氏过程和调节系数的存在性,并采用递归方法得到了模型的破产概率的上界估计.     

基于聚类分析和Cobb-Douglas函数的我国人才经济贡献率测算

建立人才环境综合评价指标体系,对指标体系进行因子分析,根据各个主因子得分,通过聚类将中国(除港澳台以外的)31个省(市、自治区)划分为若干类别;对于每一类别,分别构建物质资本、人才资本、一般人力资本等到经济产出之间的改进柯布道格拉斯生产函数模型,得到不同类别地区人才对经济增长的贡献率,进而计算全国人才对经济增长贡献率的总体水平.研究表明:2001-2010年期间,31个地区按照人才环境可分为3类.第一类地区包括北京、上海、天津,人才环境发展水平最高,人才经济贡献率为27.13%;第二类地区包括广东、浙江等东部沿海6个省份,人才环境发展水平居中,人才经济贡献率为24.91%;第三类地区为其余22各省份,人才环境发展水平偏低,人才经济贡献率为18.78%.全国人才经济贡献率总体水平为22.68%.     

解析法确定含蜡原油热质耦合的蜡分子扩散速率

蜡分子扩散过程是在热和质的广义热力学"力"耦合驱动下产生广义热力学"流"的结果,其实质是传热和传质同时存在的复杂耦合不可逆过程.基于非平衡态热力学的基本原理,推导出含蜡原油管输过程蜡分子扩散热质传递的线性唯象方程组;依据质量和能量的守恒关系,得到蜡分子扩散的传热一传质微分方程组,利用拉普拉斯变换求解到其解析解,探讨促使蜡分子扩散的动力学原因,分析输量和季节变化的不同工况对扩散速率的影响.     

比例延迟微分方程的连续有限元法

利用连续有限元法求解比例延迟微分方程,在一致网格下,给出比例延迟微分方程连续有限元解的整体收敛阶,数值实验验证了理论结果的正确性.