带有可变库存费用和短缺的变质性物品的经济批量模型

传统的经济批量模型通常都假定物品的库存费用是固定不变的.放松了这个假定,通过考虑库存费用的两种可能变化情形即(A)库存费的变化率为存储时间的函数;(B)库存费的变化率为库存量的函数,并在需求线性依赖于库存水平的形式下,发展了两个变库存费的变质性物品的经济批量模型.在模型中允许短缺发生且假定短缺完全拖后,理论上证明了模型具有唯一的整体最优解,揭示了库存费的变化对库存系统最优订货策略的影响.     

不确定条件下工程项目的多目标模糊均衡优化

在工程项目多目标优化问题研究基础上,研究不确定环境下工程项目多目标均衡优化问题.利用模糊数表示费用变化率和质量变化率,考虑模糊集的不同可能性水平,建立工程项目多目标模糊均衡优化模型,给出模型的求解方法和步骤,得到不同可能性水平下多目标优化问题的最优折衷解变化范围.优化方法使决策者能够根据决策风险的大小进行最优目标值的确定.     

非线性对流扩散问题的变网格特征有限元方法

本文讨论一类非线性对流扩散问题的变网格特征有限元方法,其数学模型是 我们提出应用特征有限元方法求解上述问题,并利用变网格技巧以减少计算工作量。此方法的优点在于问题的解沿特征方向τ的变化率远慢于t方向的变化率,从而我们的格式可用于较大的时间步长过程。彩依赖于时间t的变网格技巧,在解的变化剧     

一类系数依赖于时间的抛物系统解的全局存在性及爆破现象

研究了系数依赖于时间的抛物系统解的爆破现象.应用微分不等式技术,得到了一类系数依赖于时间的抛物系统存在全局解的条件.当系统的数据项满足不同的适当约束条件时,推导了爆破时间的上下界.     

非线性抛物问题熵解的某些定性性质

本文研究了非线性抛物问题熵解的正性依赖于初始资料和方程右端项的正性以及熵解的稳定性依赖于方程右端项的弱L1摄动.     

带有可变库存费的变质性物品的部分延期供给的库存控制模型

传统的库存控制模型都视需求率为常数,在这篇文章中,放松了这个假定,研究了库存费的两种可能的变化:(i)库存费的变化率为存储时间的函数;(ii)库存费的变化率为库存量的函数.在模型中允许短缺发生且假定短缺部分延期供给,且在需求率线性依赖于库存水平的情形下,发展了两个变库存费的库存控制模型.     

具有多平衡解的种群模型平衡解的吸收域

考虑具有多平衡解的种群动力系统模型 ,在讨论各平衡解渐近性质的基础上 ,通过对种群育龄区间的分析 ,证明了平衡解对初值的连续依赖性 ,给出了各平衡解的吸收域 .     

广义对称对策的核仁

Schmeidler于1969年提出了核仁的概念,并把它作为合作对策的一种解,同时证明了核仁对每个对策存在唯一,且连续地依赖于对策的特征函数.1977年,Justman运用点到集映射讨论了一般n人合作对策的核仁求解问题.1981年,Dragan从平衡集入手,在理论上给出了通过解一系列线性规划而求出n人合作对策的核仁的一种算法.但是,实际上有效而可行的求解一般合作对策的核仁的算法还没有.然而,也有许多人对某类     

泛函微分方程的发展和应用

用常微分方程作为数学模型的系统仅有一个自变量,在大多数场合它表示时间.这类问题实质上都假定事物的未来状态仅由当前的状态决定而不依赖于它的过去历史.确切地说,若方程满足解的存在唯一性条件,则解在某时刻之值便完全决定这个解.但是,早在十八世纪就已发现某种例子并非如此,它们的未来状态不仅取决于当前的状态而且还取决于过去一段时间中的状态,甚至依赖于状态的变化率.所导出的微分方程不仅含有自变元t,而且含有不同于t的“偏差变元”d(t),通常总是把d(t)记为t—τ(t),τ(t)叫做偏差,这不同于常微分方程,而d(t)又非新的独立变量,所以它又不是通常意义下的偏微分方程.τ为常数的情形是最基本的,一般则为t的函数,甚至是解及其导数的函数.它可以是有限个,可数无限个或者以连续分布的方式包含于某类积分微分方程之中.近     

具有Neumann边界的抛物型方程组的反馈能稳性

该文研究了一类半线性抛物型方程组平衡解的有限维反馈能稳性, 控制器由对应于平衡解的线性化系统的LQ问题所导出. 该文发现在受控系统中如何施加控制是与平衡解有关的, 对于不同的平衡解, 在受控系统中应施加不同的控制.     

Dynamics of a predator–prey system with inducible defense and disease in the prey

Establishing and researching a population dynamical model based on the differential equation is of great significance. In this paper, a predator–prey system with inducible defense and disease in the prey is built from biological evolution and Eco-epidemiology. The effect of disease on population stability in the predator–prey system with inducible defense is studied. Firstly, we verify the positivity and uniform boundedness of the solutions of the system. Then the existence and stability of the equilibria are studied. There are no more than nine equilibrium points in the system. We use a sophisticated parameter transformation to study the properties of the coexistence equilibrium points of the system. A sufficient condition is established for the existence of Hopf bifurcation. Numerical simulations are performed to make analytical studies more complete.     

Stability and travelling waves for a time-delayed population system with stage structure

We study a time-delayed population system with stage structure for the interaction between two species, the adult members of which are in competition. For each of the two species the model incorporates a time delay which represents the time from birth to maturity of that species. The global stability results are established for each equilibrium. The criteria for global convergence to each equilibrium are sharp and involve these delays. By using lower and upper travelling wave solutions, we show that the model has travelling wave solutions that connect the origin and the coexistence equilibrium with speeds greater than the spreading speed of each species in the absence of its rival.     

Threat bargaining games with a variable population

In this paper we establish links between desirable properties satisfied by familiar solutions to bargaining games with a variable population and the Nash equilibrium concept for threat bargaining games. We introduce three new concepts for equilibrium threat strategies called strategic stability, strategic monotonicity with respect to changes in the number of agents and strategic constancy. Our primary objective in this paper is to show that familiar assumptions satisfied by bargaining games with a variable population yield equilibrium threat strategies which satisfies in a very natural way the concepts we have introduced.     

A Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge

In this paper, a predator–prey Leslie–Gower model with disease in prey has been developed. The total population has been divided into three classes, namely susceptible prey, infected prey and predator population. We have also incorporated an infected prey refuge in the model. We have studied the positivity and boundedness of the solutions of the system and analyzed the existence of various equilibrium points and stability of the system at those equilibrium points. We have also discussed the influence of the infected prey refuge on each population density. It is observed that a Hopf bifurcation may occur about the interior equilibrium taking refuge parameter as bifurcation parameter. Our analytical findings are illustrated through computer simulation using MATLAB, which show the reliability of our model from the eco-epidemiological point of view.     

The fractional-order SIS epidemic model with variable population size

In this work, we deal with the fractional-order SIS epidemic model with constant recruitment rate, mass action incidence and variable population size. The stability of equilibrium points is studied. Numerical solutions of this model are given. Numerical simulations have been used to verify the theoretical analysis.     

Hierarchical Discrete Models of Competition for a Resource

A coupled pair of first order nonlinear discrete hierarchical age-structured models are applied to study two modes of intraspecific competitions; scramble and contest. The study focuses on several comparisons of the dynamical outcomes of the two competitions. For a constant resource, it is shown, using analytical and numerical approaches, that solutions of the contest model monotonically equilibrate, while solutions of the scramble model oscillate and become chaotic. It is also shown that the inherent net reproductive number of each population affects the comparison of equilibrium points in the two populations. By considering cases on the resource and model parameters, the local as well as the global stability of nontrivial equilibrium points are studied. The impact of a contest and a scramble consumer on a time dependent resource is considered numerically.     

种群生理结构模型解的性质

考虑具有生长率的种群生理结构动力学模型,讨论了系统解的渐近性质,当系统具有多平衡解时,指出各平衡解的稳定性。     

Hopf bifurcation analysis in a multiple delayed innovation diffusion model with Holling II functional response

A nonlinear mathematical model with Holling II functional response describing the dynamics of nonadopter and adopters population in a stage structured innovation diffusion model, which incorporates the evaluation stage (multiple delays), is proposed. Firstly, we study the stability and the existence of periodic solutions via Hopf bifurcation with respect to both delays at the positive equilibrium by analyzing the distribution of the roots of the corresponding exponential characteristic equation obtained through the variational matrix. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined with the help of normal form theory and center manifold theorem. Meanwhile, various cases are discussed to examine the effect of different delays on the stability of delayed innovation diffusion system and are also established numerically. It is also observed that the cumulative density of external influences has a significant role in developing maturity stage (adoption stage) in the system. Finally, numerical simulations are carried out to support and supplement the analytical findings.     

Local and global bifurcations in an SIRS epidemic model

This paper studies the existence and stability of the disease-free equilibrium and endemic equilibria for the SIRS epidemic model with the saturated incidence rate, considering the factor of population dynamics such as the disease-related, the natural mortality and the constant recruitment of population. Analytical techniques are used to show, for some parameter values, the periodic solutions can arise through the Hopf bifurcation, which is important to carry different strategies for the controlling disease. Then the codimension-two bifurcation, i.e. BT bifurcation, is investigated by using a global qualitative method and the curves of saddle-node bifurcation, Hopf bifurcation and homoclinic bifurcation are obtained at the degenerate equilibrium. Moreover, several numerical simulations are given to support the theoretical analysis.