Mathematical model for the control of a pest population with impulsive perturbations on diseased pest

In this paper, a stage-structured pest management SI model with impulsive perturbations on infected pest is introduced. Sufficient conditions of the global attractivity of pest-extinction periodic solution and permanence of the system are obtained. We also prove that all solutions of system are uniformly ultimately bounded.     

The optimal pricing and ordering policy for an integrated inventory model when trade credit linked to order quantity

In traditional inventory models, it is implicitly assumed that the buyer must pay for the purchased items as soon as they have been received. However, in many practical situations, the vendor is willing to provide the buyer with a permissible delay period when the buyer’s order quantity exceeds a given threshold. Therefore, to incorporate the concept of vendor–buyer integration and order-size-dependent trade credit, we present a stylized model to determine the optimal strategy for an integrated vendor–buyer inventory system under the condition of trade credit linked to the order quantity, where the demand rate is considered to be a decreasing function of the retail price. By analyzing the total channel profit function, we developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer’s order quantity, and the numbers of shipment per production run from the vendor to the buyer. Numerical examples and sensitivity analysis are given to illustrate the theoretical results, and some managerial insights are also obtained.     

Stability of singularly perturbed switched systems with time delay and impulsive effects

This paper studies the stability properties of singularly perturbed switched systems with time delay and impulsive effects. Such systems are assumed to consist of both unstable and stable subsystems. By using the multiple Lyapunov functions technique and the dwell time approach, some stability criteria are established. Our results show that impulses do contribute in order to obtain stability properties even when the system consists of only unstable subsystems. Numerical examples are presented to verify our theoretical results.     

An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity

To attract more sales suppliers frequently offer a permissible delay in payments if the retailer orders more than or equal to a predetermined quantity W. In this paper, we generalize [Goyal, S.K., 1985. EOQ under conditions of permissible delay in payments. Journal of the Operational Research Society 36, 335–338] economic order quantity (EOQ) model with permissible delay in payment to reflect the following real-world situations: (1) the retailer’s selling price per unit is significantly higher than unit purchase price, (2) the interest rate charged by a bank is not necessarily higher than the retailer’s investment return rate, (3) many items such as fruits and vegetables deteriorate continuously, and (4) the supplier may offer a partial permissible delay in payments even if the order quantity is less than W. We then establish the proper mathematical model, and derive several theoretical results to determine the optimal solution under various situations and use two approaches to solve this complex inventory problem. Finally, a numerical example is given to illustrate the theoretical results.     

具有脉冲收获的捕食系统的周期解

考虑了一类具有阶段结构和脉冲收获的捕食模型.讨论了解的非负性和有界性.利用重合度定理,得到了正周期解存在的充分条件.     

一类奇摄动微分——差分反应扩散方程

奇摄动问题有很强的自然科学的背景,它在生态环境、大气物理、海洋科学、催化反应、激波和量子物理中都有很广泛的应用.本文研究了一类带有小延迟的微分--差分反应扩散方程初值问题.在适当的条件下,利用奇摄动伸长变量法,构造了问题的形式渐近解.再用微分不等式理论证明了解的一致有效性.     

城市交通信号实时控制问题

以车辆平均延误时间最小为目标,建立单交叉口和线状区域的多交叉口信号实时配置的优化模型,结合外点罚函数法和模式搜索法求解,解决函数的不可微问题,算法简单可行.     

一类具有离散时滞的非自治扩散的两种群模型的一致持续生存

持续生存概念是种群生态系统稳定性的一个重要描述,而研究竞争种群共存的问题是种群生态学的一个重要问题.进一步考虑具有离散时滞的非自治的两种群竞争扩散摸型,使模型更符合其生态意义,通过微分不等式获得了其一致持续生存的充分条件.     

高维无穷时滞脉冲积分微分方程概周期解的存在唯一性

研究一类高维无穷时滞的非线性脉冲积分微分方程x′(t)=A(t)x(t)+∫-t∞C(t,s)g(s,x(s))ds+f(t,x(t-τ))+b(t),t≠tkΔx(t)=Bkx(t)+Ik(x(t))+γk,t=tk,k∈Z概周期解的存在性、唯一性问题.利用不动点原理和线性系统的指数二分性理论,建立了保证其概周期解存在性、唯一性的充分条件,得到了一些新的结果.     

具有输入时滞的时滞关联不确定系统的鲁棒分散控制

研究了一类同时具有输入时滞以及不确定参数的时滞关联大系统的稳定性问题.基于所谓的还原法,给出一种新的状态反馈控制器的设计方法,这种方法的不同之处在于利用了时延的大小以及反馈控制的历史信息.根据Lyapunov稳定性理论得到了系统在控制器作用下稳定的充分条件,所有条件都化成可解的标准LMIs(Linear matrix inequalities)形式.文章最后给出了一个数值例子说明本文结果的可行性.