内生网络环境下具有异质连接费用的局部策略互动

考察内生网络环境下局中人之间的局部策略互动, 网络中的局中人只与直接邻居进行协同对策. 网络生成的过程中, 建立连接的费用是异质的~(具有两种水平), 与采取有效行动的局中人建立连接时执行高水平费用, 与采取风险占优行动的局中人建立连接时执行低水平费用. 在异质连接费用的情形下, 首次较为完整地给出了均衡网络的结构特性和局中人的行动选择, 并分析了费用参数对均衡结果的影响.     

内生无限平面网格上基于策略互动的均衡网络结构及吸收集

在内生网络环境下,基于局中人的策略互动研究了均衡网络的结构特性,以及局中人策略选择的倾向性. 在动态进程的同一阶段,规定所有局中人同时进行策略更新,研究了网络生成的连接费用、互动支付等参数之间的相互关系及其对均衡结构或吸收集的影响. 主要贡献是将网络的内生性与无限网格上的策略互动联系在一起,得出不同连接费用水平之下的均衡结构、吸收集的准确特征.     

碳减排政策下多周期供应链网络均衡决策

为研究碳减排政策对多周期供应链网络均衡决策的影响,分析了供应链网络结构中各层的最优条件,建立了多周期碳减排供应链网络均衡模型.首先将其转化为等价的变分不等式问题,然后利用变分不等式的投影收缩算法进行求解.并通过模型仿真分析了在不同周期下不同碳限额、单位碳排放量对供应链网络均衡的影响结果发现企业在环境绩效和经济绩效之间存在冲突,适当的控制碳税和调整产品的单位碳排放量可以缓解这种冲突.同时,政府对于碳限额的值过于宽松,对于碳减排的实施起不到明显作用.     

考虑零售商库存能力约束的供应链网络均衡模型研究

在考虑零售商库存能力约束情形下,研究了多个竞争的零售商与供应商组成的供应链网络均衡问题.通过对供应链各层级的供应商、零售商、消费市场最优性条件的分析,利用变分不等式构建了供应链网络均衡模型.最后,运用投影收缩算法对均衡模型进行求解,并仿真分析了零售商库存能力约束对网络成员及整个供应链网络的影响.     

基于复杂网络理论的含分布式发电的电力网络脆弱度评估

基于复杂网络理论研究含分布式发电(DG, Distributed Generation)的电力网络脆弱度评估问题,有针对性地提出三类脆弱度评估指标,其中基于结构的脆弱度指标能够体现网络拓扑和节点功率对系统供电效率的影响;攻击脆弱度指标可用于评估系统抵御节点和线路移除的能力;基于运行方式的脆弱度指标能够反映整个电网有功功率在传输距离上的均衡度.仿真算例验证了所提指标的有效性和DG对于改善系统功率传输性能与提高抗干扰能力方面的作用.     

多社团加权复杂网络建模及其级联抗毁性研究

为了研究社团结构和权重因素对网络级联抗毁性的影响,引入节点和边的消亡机制,建立了一类具有社团结构的加权网络模型.采用本方法生成网络的度、强度和边权分布都呈现无标度特性,比现有BBV (Barrat-Barthelemy-Vespignani)模型具有更好的社团结构特性,且幂律指数、模块度参数可调.在此基础上研究了网络的级联抗毁性,采用节点及其邻居节点强度的函数定义网络负荷,故障节点负荷采用"局部定义,局部分配"的策略.仿真分析了边权演化参数、模块度函数、攻击策略和演化时间对网络级联抗毁性的影响.结论表明,网络的抗毁性与边权演化参数、网络演化时间成反比,与模块度的关系不是单调的而是存在一个阈值.优先攻击度最大节点的策略对网络抗毁性破坏最大,且在多节点遭受攻击时,网络的故障规模会发生突变.文章的研究结论对故障的预防与控制以及网络的建设具有一定的参考价值.     

基于网络混合学习策略的股市投资者行为演化模型及仿真

针对投资者有限理性决策行为的模仿学习等特质,运用复杂网络、贝叶斯学习和社会学习理论,分别对个人投资者和机构投资者的投资行为决策机制进行系统性分析,由此构建基于网络混合学习策略的投资者行为演化机理和数理模型,并进行数理解析和模拟仿真。研究发现,投资者金融关联网络的拓扑结构对个人投资者行为动态演变具有较强影响,但对机构投资者的影响较弱;个人投资者的学习策略偏好影响其行为动态演变均衡状态的稳定性较为显著;机构投资者获取的私有信息精确度与其行为动态演变的均衡状态之间存在显著的非线性关联;投资者的初始行为状态对其投资行为动态演变均衡状态的影响效应均较弱。     

基于惩罚与补贴的再制造闭环供应链网络均衡模型

为研究我国废旧电子产品(WEEE)立法的问题,分析了供应商、制造商、零售商、需求市场及回收商的行为,分别建立了变分不等式模型,并在此基础上建立了五级再制造闭环供应链网络均衡模型。模型考虑了政府对于制造商的惩罚政策与对于回收商的补贴政策。通过修正投影算法求解算例,仿真分析了旧材料转化率、回收率、惩罚及补贴政策对闭环供应链网络均衡结果的影响。结果表明,随着政府对于回收商的补贴的增加,不但回收商的回收量提高,闭环供应链的新材料需求量、旧材料需求量、销售量均增加;相反,随着政府对于制造商未完成的回收量的罚款增加,回收量、新材料需求量、旧材料需求量、销售量均降低;追求高回收率的政策并不总是有效的;而提高WEEE的旧材料转化率对于闭环供应链有利。     

随机需求下三度价格歧视重复博弈的研究

基于随机需求函数,讨论了相互竞争的两厂商实施三度价格歧视无限次重复博弈和不定次重复博弈的均衡分析,在三度价格歧视无限次重复博弈分析中,得出了两厂商在贴现因子影响下的子博弈完美纳什均衡.在三度价格歧视不定次重复博弈分析中,设计了不同的方案并进行了Matlab仿真,比较了不同贴现因子下不同仿真方案的厂商得益,并对仿真结果进行了系统分析,得到了统计意义下的均衡分析.     

随机需求下考虑风险行为的闭环供应链网络均衡模型

以变分不等式和均衡理论为基本研究工具,研究了随机需求与再制造率不确定条件下多个竞争型的供应商、制造商、零售商及消费市场的行为及均衡条件。对所建立的多级闭环供应链网络均衡模型,通过拟牛顿算法求解变分不等式,并仿真分析了再制造率、回收率以及风险因素对闭环供应链网络均衡结果的影响。结果表明:制造商提高再制造率能实现供应链成员利润的增加、产品价格的降低以及回收量的增加;制造商基于风险最小化和利润最大化相结合的原则进行决策能增加产品的交易量及企业的利润。     

Spreading dynamics and global stability of a generalized epidemic model on complex heterogeneous networks

In this paper, a generalized epidemic model on complex heterogeneous networks is proposed. To give a theoretical explanation for the simulation results established on networks, mathematical analysis of the epidemic dynamics is presented via mean-field approximation. Stabilities of the disease-free equilibrium and the endemic equilibrium are studied. The results explain why the heterogeneous connectivity patterns impact the epidemic threshold and reveal how the host parameters and the underlying network structures determine disease propagation.     

Endogenous network formation in a Tullock contest

We propose a model of network formation in a Tullock contest. Agents first form their partnerships and then choose their investment in the contest. While a link improves the strength of an agent, it also improves the position of her rival. It is thus not obvious that they decide to cooperate. We characterize all pairwise equilibrium networks and find that the network formation process can act as a barrier to entry to the contest. We then analyze the impact of network formation on total surplus and find that a social planner can increase total surplus by creating more asymmetry between agents, as long as this does not reduce the number of participating agents. We show that barriers to entry may either hurt total surplus, as the winner of the prize does not exploit all the possible network benefits, or improve total surplus since less rent is dissipated when competition becomes less fierce. Finally, when networking acts as an endogenous barrier to entry, no pairwise equilibrium network is efficient.     

Analysis of epidemic spreading of an SIRS model in complex heterogeneous networks

In this paper, we study the spreading of infections in complex heterogeneous networks based on an SIRS epidemic model with birth and death rates. We find that the dynamics of the network-based SIRS model is completely determined by a threshold value. If the value is less than or equal to one, then the disease-free equilibrium is globally attractive and the disease dies out. Otherwise, the disease-free equilibrium becomes unstable and in the meantime there exists uniquely an endemic equilibrium which is globally asymptotically stable. A series of numerical experiments are given to illustrate the theoretical results. We also consider the SIRS model in the clustered scale-free networks to examine the effect of network community structure on the epidemic dynamics.     

Synchronization in complex networks with distinct chaotic nodes

We present an approach to the chaos synchronization of complex networks with distinct nodes. The chaotic synchronization is achieved by adding a derivative coupling term in the network equation. We assume that node in networks are different and are given by the Lorenz, Rössler, Chen and Sprott chaotic systems. The derivative term is capable to induce the synchronous behavior in the network. Moreover such a coupling leads the global behavior to a chaotic attractor. We found that without derivative coupling the network is leaded only to an equilibrium point or a limit cycle. Numerical simulations are provided to illustrate the result. Complementary the network synchrony can be chaotic in presence of the derivative coupling.     

Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks

We formulate discrete-time analogues of integrodifferential equations modelling bidirectional neural networks studied by Gopalsamy and He. The discrete-time analogues are considered to be numerical discretizations of the continuous-time networks and we study their dynamical characteristics. It is shown that the discrete-time analogues preserve the equilibria of the continuous-time networks. By constructing a Lyapunov-type sequence, we obtain easily verifiable sufficient conditions under which every solution of the discrete-time analogue converges exponentially to the unique equilibrium. The sufficient conditions are identical to those obtained by Gopalsamy and He for the uniqueness and global asymptotic stability of the equilibrium of the continuous-time network. By constructing discrete-time versions of Halanay-type inequalities, we obtain another set of easily verifiable sufficient conditions for the global exponential stability of the unique equilibrium of the discrete-time analogue. The latter sufficient conditions have not been obtained in the literature of continuous-time bidirectional neural networks. Several computer simulations are provided to illustrate the advantages of our discrete-time analogue in numerically simulating the continuous-time network with distributed delays over finite intervals.     

Supply chain network equilibrium with strategic financial hedging using futures

In this paper, we develop a network equilibrium model for supply chain networks with strategic financial hedging. We consider multiple competing firms that purchase multiple materials and parts to manufacture their products. The supply chain firms’ procurement activities are exposed to commodity price risk and exchange rate risk. The firms can use futures contracts to hedge the risks. Our research studies the equilibrium of the entire network where each firm optimizes its own operation and hedging decisions. We use variational inequality theory to formulate the equilibrium model, and provide qualitative properties. We provide analytical results for a special case with duopolistic competition, and use simulations to study an oligopolistic case. The analytical and simulation studies reveals interesting managerial insights.     

A simplified recurrent neural network for pseudoconvex optimization subject to linear equality constraints

In this paper, the optimization techniques for solving pseudoconvex optimization problems are investigated. A simplified recurrent neural network is proposed according to the optimization problem. We prove that the optimal solution of the optimization problem is just the equilibrium point of the neural network, and vice versa if the equilibrium point satisfies the linear constraints. The proposed neural network is proven to be globally stable in the sense of Lyapunov and convergent to an exact optimal solution of the optimization problem. A numerical simulation is given to illustrate the global convergence of the neural network. Applications in business and chemistry are given to demonstrate the effectiveness of the neural network.     

Stability Analysis of Gradient-Based Neural Networks for Optimization Problems

The paper introduces a new approach to analyze the stability of neural network models without using any Lyapunov function. With the new approach, we investigate the stability properties of the general gradient-based neural network model for optimization problems. Our discussion includes both isolated equilibrium points and connected equilibrium sets which could be unbounded. For a general optimization problem, if the objective function is bounded below and its gradient is Lipschitz continuous, we prove that (a) any trajectory of the gradient-based neural network converges to an equilibrium point, and (b) the Lyapunov stability is equivalent to the asymptotical stability in the gradient-based neural networks. For a convex optimization problem, under the same assumptions, we show that any trajectory of gradient-based neural networks will converge to an asymptotically stable equilibrium point of the neural networks. For a general nonlinear objective function, we propose a refined gradient-based neural network, whose trajectory with any arbitrary initial point will converge to an equilibrium point, which satisfies the second order necessary optimality conditions for optimization problems. Promising simulation results of a refined gradient-based neural network on some problems are also reported.     

Goodwill hunting and profit sharing: Decision-making in a newspaper chain

A generalised equilibrium solution to the stochastic two-echelon newsvendor problem is achievable when formulated in the context of some cooperation and coordination between the primal (retailer) and dual (manufacturer) operators. We build on previous work detailing this equilibrium solution and apply it to the newspaper business. The solution incorporates changes in variability encountered due to promotional activity which extends the efficient frontier. We also consider consequences for profit and goodwill costs of identifying an equilibrium solution when additional income is generated from a source outside of the supply chain, such as advertising. We generalise to the supply chain network where there is some knowledge of demand or supply distributions further up or down the supply chain. We find that the primal–dual formulation and equilibrium solution apply to interactions between components of supply chain networks and illustrate with the transition to the direct distribution of newspapers.     

Epidemic spreading of an SEIRS model in scale-free networks

An SEIRS epidemic model on the scale-free networks is presented, where the active contact number of each vertex is assumed to be either constant or proportional to its degree for this model. Using the analytical method, we obtain the two threshold values for above two cases and find that the threshold value for constant contact is independent of the topology of the underlying networks. The existence of positive equilibrium is determined by threshold value. For a finite size of scale-free network, we prove the local stability of disease-free equilibrium and the permanence of the disease on the network. Furthermore, we investigate two major immunization strategies, random immunization and targeted immunization, some similar results are obtained. The simulation shows the positive equilibrium is stable.