事件故障状态量子博弈过程的参与者收益研究

为了解事件故障状态量子博弈过程中参与者收益随各影响因素的变化情况,提出在空间故障树(Space Fault Tree, SFT)框架内,以事件故障状态为对象,对参与者收益进行研究。事件故障状态使用量子态表示,管理者和操作者的不同行为对事件故障状态的作用使用博弈表示。考虑因素包括安全产出价值、安全收益分配系数、安全措施成本。研究了事件故障状态与量子博弈的关系;纠缠与非纠缠态下的参与者收益;参与者收益受到各因素影响的特征等。研究得到了管理者和操作者考虑纠缠和非纠缠态的收益函数。结合SFT理论方法,提出了针对收益的因素重要度、因素联合重要度、收益风险区和安全区、因素区域重要度。理论上SFT可用于量子博弈参与者收益的分析。也论述了使用因素空间理论解决该问题的可能性。     

三体量子系统辅助纠缠的无损解耦

Hilbert空间及其张量理论是多体量子系统的数学框架.多体系统量子纠缠的无损解耦问题是当前量子信息与计算理论的前沿课题之一.这一课题主要研究的是在何种条件下多体纠缠是可以被无损解耦的,目前已知的无损解耦条件是在三量子比特系统情形获得的.本文主要是推广以上纠缠无损解耦结论于更一般的三体系统,证明了对于某些满足特定条件的2?2?3和2?2?4系统上的纯态,可以实现无损解耦.     

相位阻尼信道条件下量子斗鸡博弈模型均衡解分析

利用量子博弈的相关理论,以噪音强度和记忆强度为参量,建立了相位阻尼信道条件下的量子斗鸡博弈模型,求出了模型的量子纳什均衡解,讨论了两参量对均衡解稳定性的影响,得出在无记忆相位阻尼信道条件下,当噪音强度小于阈值0.24时,纳什均衡仍然为帕累托最优解,当噪音强度大于0.24时,均衡解演变为另2个均衡解,不再是帕累托最优;在有记忆相位阻尼信道条件下,当噪音强度小于0.24,且记忆强度大于0.5时,均衡解是稳定的.特殊地,当信道是完全记忆时,均衡解的稳定性与噪音强度无关.     

量子博弈理论与自主创新能力研究

表现为经济上的综合竞争实力的自主创新能力和产生于博弈论和量子信息结合的量子博弈理论与经济学、经济物理学息息相关。文章探讨了量子博弈理论与自主创新能力之间关系；分析了量子博弈理论与自主创新能力在结构上的相似性，指出了二者理论的共同之处，明确自主创新能力和量子博弈理论构成要素和理论体系及应用上的相同的核心共性；分析了量子博弈理论与自主创新能力在策略关联、非确定结果描述和合作关系三个方面的关系，表明量子博弈理论可以准确地描述和解决自主创新在这三个方面的问题。     

碳税机制下考虑不同低碳策略的动态博弈模型及复杂性研究

考虑碳排放税,建立双寡头制造商分别实施废品回收和绿色低碳广告投入策略的动态博弈模型。通过系统稳定域,分岔图,功率谱等分析了博弈模型纳什均衡解处的稳定性及参数对系统稳定域的影响,同时对系统的复杂性特征进行了研究。结果表明,消费者回收价格敏感性增加会使整个系统稳定域缩小,而绿色低碳广告投入水平增加只会使实施该策略的企业自身稳定域扩大;当制造商价格调整速度过快时,系统会进入混沌状态;混沌状态下,对比实施广告策略的制造商,实施废品回收策略的制造商价格调整行为对市场造成的震荡更大。最后使用反馈控制策略对系统混沌状态进行了有效的控制,研究结果对制造商低碳策略选择及价格决策有着较好的借鉴意义。     

平面不可压缩磁流体动力学五模类Lorenz方程组的动力学行为及其数值仿真北大核心CSCD

该文研究了平面正方形区域上不可压缩的磁流体动力学方程组五模截断所得到的十维模型的动力学行为问题.首先,利用模式截断方法推导了十模系统,讨论了该方程组定常解及其稳定性,其次,发现了Hopf分叉和混沌,证明了该方程组吸引子的存在性和全局稳定性,最后,给出了系统从分叉到混沌整个过程所呈现的动力学行为演变的详细数值模拟结果,分析了磁性对系统动力学行为的影响.基于分岔图、Lyapunov指数谱和庞加莱截面图,返回映射和功率谱等数值模拟结果揭示了这个低维系统的动力学行为特征.这个新混沌系统通过周期倍分岔过渡到混沌(费根鲍姆途径).     

平面不可压缩磁流体动力学五模类Lorenz方程组的动力学行为及其数值仿真

该文研究了平面正方形区域上不可压缩的磁流体动力学方程组五模截断所得到的十维模型的动力学行为问题.首先,利用模式截断方法推导了十模系统,讨论了该方程组定常解及其稳定性,其次,发现了Hopf分叉和混沌,证明了该方程组吸引子的存在性和全局稳定性,最后,给出了系统从分叉到混沌整个过程所呈现的动力学行为演变的详细数值模拟结果,分析了磁性对系统动力学行为的影响.基于分岔图、Lyapunov指数谱和庞加莱截面图,返回映射和功率谱等数值模拟结果揭示了这个低维系统的动力学行为特征.这个新混沌系统通过周期倍分岔过渡到混沌(费根鲍姆途径).     

原子核自旋陀螺仪的基本原理

介绍了一种基于K-~3He comagetometer原理的新型核自旋陀螺仪.这种陀螺仪精度提高的空间大,因此对它的研究具有重要意义.在comagnetometer中,系统状态演化的方程较为复杂,在简化的Bloch绘景下,给出了comagnetometer的输出信号与陀螺仪转动角度的关系.最后,将系统状态演化的方程推广到量子滤波方程,通过连续测量和量子反馈控制的方法,达到提高系统的稳定性和测量灵敏度的目的.     

一类具有阶段结构的食物链系统

研究了一类具有阶段结构的食物链模型,分析了系统平衡点的稳定性,运用数值模拟展示了系统周期性振动,混沌等复杂的动力学行为,并分析了阶段结构对系统复杂行为的影响.     

新三维自治混沌系统动力学性质研究

采用动力系统理论分析和计算机数值仿真相结合的方法,研究了一类新三维自治混沌系统的非线性动力学行为,如平衡点及其稳定性、不变集、混沌吸引子、吸引域等,从而展示了该混沌系统的丰富的动力学特性并且用matlab给出了相应的计算机模拟.创新点在于同时考虑了该混沌系统的最终界和全局吸引集,并且对于这个混沌系统的任意正参数,分别得到了该混沌系统最终界的一个参数族数学表达式和全局指数吸引集的一个参数族数学表达式,最后利用交集的思想分别得到了混沌系统最终界和全局吸引集的一个较小的数学表达式.混沌系统有望在实际保密通信中得到应用.     

Complex dynamics and chaos control of duopoly Bertrand model in Chinese air-conditioning market

A dynamic duopoly Bertrand model with quadratic cost function which is closer to reality and different from previous researches is discussed. The model is applied into air-conditioning market where the boundary equilibrium point is locally stable. Numerical simulations illustrate that the stability of Nash equilibrium strongly depends on the speed of adjustment of bounded rational player. The adjustment speeds and the degree of substitutability may undermine the stability of the equilibrium and cause a market structure to behave chaotically. The Lyapunov dimension of the chaos attractor is 1.9585 under some conditions. The stabilization of the chaotic behavior can be obtained by reducing the degree of substitutability. The results have an important theoretical and practical significance to Chinese air-conditioning market.     

The dynamics of Bertrand model with bounded rationality

The paper considers a Bertrand model with bounded rational. A duopoly game is modelled by two nonlinear difference equations. By using the theory of bifurcations of dynamical systems, the existence and stability for the equilibria of this system are obtained. Numerical simulations used to show bifurcations diagrams, phase portraits for various parameters and sensitive dependence on initial conditions. We observe that an increase of the speed of adjustment of bounded rational player may change the stability of Nash equilibrium point and cause bifurcation and chaos to occur. The analysis and results in this paper are interesting in mathematics and economics.     

The dynamics of a Bertrand duopoly with differentiated products: Synchronization,intermittency and global dynamics

We study the dynamics of a duopoly game à la Bertrand with horizontal product differentiation as proposed by Zhang et al. (2009) [35] by introducing opportune microeconomic foundations. The final model is described by a two-dimensional non-invertible discrete time dynamic system T. We show that synchronized dynamics occurs along the invariant diagonal being T symmetric; furthermore, we show that when considering the transverse stability, intermittency phenomena are exhibited. In addition, we discuss the transition from simple dynamics to complex dynamics and describe the structure of the attractor by using the critical lines technique. We also explain the global bifurcations causing a fractalization in the basin of attraction. Our results aim at demonstrating that an increase in either the degree of substitutability or complementarity between products of different varieties is a source of complexity in a duopoly with price competition.     

Bifurcations and chaos in a nonlinear discrete time Cournot duopoly game

A nonlinear discrete time Cournot duopoly game is investigated in this paper. The conditions of existence for saddle-node bifurcation, transcritical bifurcation and flip bifurcation are derived using the center manifold theorem and the bifurcation theory. We prove that there exists chaotic behavior in the sense of Marotto＇s definition of chaos. The numerical simulations not only show the consistence with our theoretical analysis, but also exhibit the complex but interesting dynamical behaviors of the model. The computation of maximum Lyapunov exponents confirms the theoretical analysis of the dynamical behaviors of the system.     

Dynamics and chaos control of a duopolistic Bertrand competitions under environmental taxes

Annals of Operations Research - This paper investigates the difference between price and quantity competition in a mixed duopoly game. We describe the behavior of a duopolistic Bertrand competition...     

Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game

A dynamic of a nonlinear Kopel duopoly game with heterogeneous players is presented. By assuming two heterogeneous players where one player use naive expectation whereas the other employs a technique of adaptive. The stability conditions of equilibrium points are analyzed. Numerical simulations are used to show bifurcation diagrams, phase portraits and sensitive dependence on initial conditions. The chaotic behavior of the game has been controlled by using feedback control method.     

Dynamic Model of R&D,Spillovers, and Efficiency of Bertrand and Cournot Equilibria

Using an infinite-horizon two-player differential game, we derive and compare Bertrand and Cournot equilibria for a differentiated duopoly engaging in the process of R&D competition. The main findings of this study are as follows. First, Bertrand competition is more efficient if either R&D productivity is low or products are very different. Second, Cournot competition is more efficient provided that R&D productivity is high, products are close substitutes, and spillovers are not close to zero. This last result is different from what has been obtained in the literature. Hence, this shows that considering a dynamic model and more general investment costs does have an impact on the efficiency results.     

汽车生产厂家的定价策略博弈模型

讨论了企业在经营管理中的最优化问题,构建了汽车行业在寡头垄断市场中各厂商之间的定价博弈模型.利用统计学中的多元线性回归模型给出两种不同型号汽车的销售量和价格的经验的需求函数关系式,检验了此模型的拟合优度,对其整体显著性的进行了F检验,并对偏回归系数的显著性进行了t检验,探讨了两寡头垄断企业的产品的需求函数为二元线性函数的伯特兰德模型,获得了其纳什均衡解的一般结论,并给出了某两型号汽车的定价博弈的具体均衡结果.     

Competition analysis of a triopoly game with bounded rationality

A dynamic Cournot game characterized by three boundedly rational players is modeled by three nonlinear difference equations. The stability of the equilibria of the discrete dynamical system is analyzed. As some parameters of the model are varied, the stability of Nash equilibrium is lost and a complex chaotic behavior occurs. Numerical simulation results show that complex dynamics, such as, bifurcations and chaos are displayed when the value of speed of adjustment is high. The global complexity analysis can help players to take some measures and avoid the collapse of the output dynamic competition game.