不动点与平衡点

介绍Brouwer不动点定理、Kakutani不动点定理与数理经济学中平衡点和博弈论中Nash平衡点存在性定理的等价性结果.     

不动点与平衡点

介绍Brouwer不动点定理、Kakutani不动点定理与数理经济学中平衡点和博弈论中Nash平衡点存在性定理的等价性结果.     

饱和发生率受媒体报道影响的SEIS模型的研究

首先,建立了一个饱和发生率受媒体影响的SEIS模型,根据正平衡点的存在性得出基本再生数R0;其次,运用Routh-Hurwitz判据定理证明了地方病平衡点在某条件下的局部渐近稳定性;最后,利用第二加性复合矩阵证明了地方病平衡点的全局稳定性.     

多时滞合作系统的稳定性与全局Hopf分支

以时滞为参数,研究了一类多时滞合作系统的正平衡点的稳定性及局部Hopf分支的存在性.在此基础上结合一般泛函微分方程的全局Hopf分支定理,讨论了该系统全局Hopf分支的存在性.     

基于阈值策略带有扩散和不连续控制项的单物种生态模型的全局稳定性分析（英文）

本文通过阈值策略(TP)研究了带有扩散的单物种生态模型的控制问题.利用一致持久性理论和Filippov理论方法,得到了新模型的正平衡点的存在性定理.通过使用耦合系统的图论方法和构建Lyapunov函数思想,得到了新模型的正平衡点唯一且全局渐进稳定的充分条件.推广了文献[6]的相关结果.     

二阶Hopfield神经网络周期解的存在性

本文讨论了一类带有时滞的二阶Hopfield神经网络周期解的存在性问题。首先利用Brouwer不动点定理证明了平衡点的存在性,通过平衡点和拉格朗日中值定理,将高阶神经网络模型转换为一阶模型,然后利用重合度理论给出了周期解存在的充分条件。     

自反Banach空间中Ky Fan点的存在性

本文对自反Banach空间证明了一个Ky Fan点的存在性定理,作为它的应用,对非合作博弈的Nash平衡点及变分不等式的解给出了几个存在性定理.     

一类具有病毒饱和增殖的病毒-免疫动力学模型的分析

在假设病毒增殖率为Michaelis-Menten函数的基础上,提出了一类病毒增殖具有饱和性的病毒与特异性免疫细胞相互作用的模型.分析发现该模型至多有两个正平衡点并会发生鞍结点分支;借助中心流形定理讨论了平衡点的局部稳定性;运用Bendixson-Dulac定理排除了周期解的存在性,进而得到模型的全局动力学性态.数值模拟显示了病毒与免疫系统相互作用的结果对初始状态的依赖性,以及在作用过程中会出现病毒载量和免疫细胞种群数量的持续振荡.     

一类含时滞的比率依赖捕食系统正平衡点的全局稳定性分析

讨论了一种食饵增长为Gilpin-Ayala型的比率依赖的食饵捕食者模型,利用第二加性复合矩阵原理证明线性化系统正轨道解的稳定性,结合系统在凸集中存在唯一的局部正平衡点,证明了正平衡点的全局渐近稳定性.结合数值模拟验证了所得结论的合理性,同时指出定理结论仅为充分条件,丰富完善了模型的动力学性质.     

多主从博弈的轻微利他平衡点问题

基于经典非合作博弈的Nash平衡点问题,结合利他主义的思想,研究了多主从博弈的轻微利他平衡点问题.通过利用Fan-Glicksberg不动点定理,对两个领导者的多主从博弈在轻微利他情况下的平衡点存在性进行了讨论和研究.     

Existence of equilibria for generalized games without paracompactness

In this paper, we first prove an existence theorem of maximal elements without any paracompactness. Then, we establish an existence theorem of equilibrium points of generalized games with infinite many players and without any paracompactness, by applying our maximal element existence theorem. Our equilibrium existence theorem answers the two questions raised by Kim [6] in the affirmative.     

本质连通区的存在性和稳定性

本文首先给出了一个统一的本质连通区的存在性定理．应用这个定理，容易地导出了不动点集和Nash平衡点集本质连通区的存在性定理．此外，还首先给出了一个统一的本质连通区的稳定性定理．     

Analysis of a bacteria-immunity model with delay quorum sensing

A bacteria-immunity model with bacterial quorum sensing is formulated, which describes the competition between bacteria and immune cells. A distributed delay is introduced to characterize the time in which bacteria receive signal molecules and then combat with immune cells. In this paper, we focus on a subsystem of the bacteria-immunity model, analyze the stability of the equilibrium points, discuss the existence and stability of periodic solutions bifurcated from the positive equilibrium point, and finally investigate the stability of the nonhyperbolic equilibrium point by the center manifold theorem.     

一个新的弱Pareto-Nash均衡点存在性结果

研究了多目标广义对策问题,通过Brouwer-Schauder-Tychonoff不动点定理,建立了弱Pareto-Nash均衡点的存在性结果,最后,通过一个例子,说明结果是新的、不能被已有的存在性结果所包含.     

The essential components of the set of equilibrium points for set-valued maps

In this article, we discuss the stability of equilibrium points for set-valued maps. We introduce the notion of essential components of the set of equilibrium points for set-valued maps and prove an existence theorem of essential components. As applications, we deduce the existence of essential components of the set of coincidence points and show that every Marchaud dynamical economy (cf. [J.P. Aubin, Dynamic Economic Theory, Springer-Verlag, 1997]) possesses at least one essential component of the set of its viable equilibrium points.     

Stationary points and equilibria

Almost all existence results in mathematical economics and game theory rely on some type of fixed point theorem. However, in many cases it is much easier to apply an equivalent stationary point theorem. In this survey paper we show for various general equilibrium and game-theoretical models the usefulness of the stationary point approach to prove existence of equilibrium. We also consider path following methods to find a stationary point and illustrate such methods by an example. Finally, we discuss some refinements of stationary points and their application to solve the problem of equilibrium selection.     

多目标大博弈中弱Pareto-Berge均衡的存在性

研究了具有任意多个局中人的非合作多目标博弈(多目标大博弈).基于一般非合作博弈中的Berge均衡概念,定义多目标大博弈中的弱Pareto-Berge均衡.进一步推广了截口定理,得到新的截口定理,并且利用这个新的截口定理证明多目标大博弈中弱Pareto-Berge均衡的存在性.多目标大博弈中弱Pareto-Nash均衡的存在性结论可作为弱Pareto-Berge均衡存在性的特例给出.     

On relative normal modes

We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. In particular, we prove that under appropriate hypotheses there exist relative periodic orbits near relative equilibria even when these relative equilibria are singular points of the corresponding moment map, i.e. when the reduced spaces are singular.     

The existence of solutions for the system of generalized vector quasi-equilibrium problems

In this paper, we study the system of generalized vector quasi-equilibrium problems which includes as special cases the system of generalized vector equilibrium problems and the system of vector quasi-equilibrium problems, and establish the existence result for its solutions by means of the Kakutani–Fan–Glicksberg fixed points theorem. As special cases, we also derive the existence results for weakly Pareto–Nash equilibrium points for multiobjective generalized game problems and multiobjective game problems.