基于GMCR-NPAWLAK混合模型的冲突分析研究

冲突分析图模型中,决策者的态度只有肯定和否定两种,实际问题中往往不止两种;新PAWLAK冲突模型(NPAWLAK模型)将冲突系统中决策者的三种态度扩展到决策争端的三种程度,符合实际情况,因而研究冲突系统中决策者的偏好排序和全局可行方案对决策者的策略选择具有重要意义。本文在NPAWLAK模型的基础上,引入冲突分析图模型理论(GMCR),提出GMCR-NPAWLAK冲突分析混合模型。该混合模型首先拓展和改进的策略优先排序法,实现了冲突系统中各决策者的客观偏好排序;同时,模型给出了全局可行方案的算法,该算法依据决策者的偏好排序分析结果找出系统的全局可行方案。最后,本文以某企业劳资关系的NPAWLAK冲突为例,对冲突系统进行建模和偏好分析,得到了冲突各方的偏好序列和全局可行方案,同时验证了混合模型的有效性。     

Global existence and stability of solution of a reaction-diffusion model for cancer invasion

In this paper, we study a mathematical model of cancer invasion proposed by Gatenby and Gawlinski. The model is a strongly coupled degenerate reaction-diffusion system. Very few mathematical results are known for this system. We investigate the global existence of classical solutions for the system by using energy estimates and the bootstrap arguments, and global asymptotic stability of equilibrium points of the system by Lyapunov functions.     

一类具有阶段结构的三次捕食者-食饵交错扩散系统的整体解

应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性,该系统是具有阶段结构的两种群Lotka-Volterra捕食者-食饵交错扩散模型的推广.通过构造Lyapunov函数给出了该系统正平衡点全局渐近稳定的充分条件.     

Dynamical modeling and attitude analysis for the spacecraft with lateral solar arrays

The dynamics and attitude motion of the three-axis stabilized spacecraft installed with lateral solar arrays is investigated in terms of the rigid-flexible coupled global modes of the system. The spacecraft consists of a rigid platform with small moment of inertia and two groups of flexible solar arrays with relatively large moment of inertia installed on the rigid rotation shafts. The rigid-flexible coupled dynamic model of the spacecraft is established by using the Hamiltonian Principle. The global mode method is employed to work out the natural frequency and global modal shapes of the rigid-flexible coupled dynamic model combined with corresponding boundary conditions. To validate the effectiveness of the analytical results obtained by global mode method, the natural frequencies and mode shapes obtained from finite element model using MSC.Patran software are used as a reference. A numerical example is given to show that the results obtained from both methods are matched very well (the relative errors of the corresponding frequencies are small enough) and the rigid motion of the platform is coupled with the vibration mode of the flexible solar arrays. This implies that the global analytical modes can be used to accurately describe the rigid-flexible coupled motion of the spacecraft. By comparing with the finite element model, the reduced dynamical model derived in terms of the global modes of the system has a lower dimension. Numerical simulations for the system with variations of parameters and dynamic responses analysis for different applied forces are performed to illustrate that, the characteristics of the model are affected by inner and external factors.     

三种群食物链交错扩散模型的整体

本文应用能量估计方法和Gagliardo-Nirenberg型不等式证明了一类强耦合反应扩散系统整体解的存在性和一致有界性，该系统是带自扩散和交错扩散项的三种群Lotka-Volterra食物链模型．通过构造Lyapunov函数给出了该模型正平衡点全局渐近稳定的充分条件．     

Coexistence and Asymptotic Periodicity in a Competition Model of Plankton Allelopathy

In this paper, the two species Lotka-Volterra competition model of plankton allelopathy from aquatic ecology is discussed. The authors study the existence of solutions to a strongly coupled elliptic system with homogeneous Dirichlet boundary conditions and consider the existence, stability and global attractivity of time-periodic solutions for a coupled parabolic equations in a bounded domain. Their results show that this model possesses at least one coexistence state if cross-diffusions and self-diffusions are weak. The existence of the positive T-periodic solutions and the global stability as well as the global attractivity for the parabolic system are also given.     

一类非自治无时滞捕食食饵模型的持久性

主要针对一类非自治食饵具有阶段结构的捕食者非密度制约的捕食食饵模型进行了分析讨论,得到了种群灭绝以及持久的积分形式的充分条件,把捕食者密度制约的一些重要结论推广到捕食者非密度制约的情形,并且通过构造Lyapunov函数得到了系统的全局吸引性,最后利用数值模拟得到了当系统持久时周期模型的全局吸引性.     

Global Qualitative Analysis for a Ratio-Dependent Predator-Prey Model with Delay

A ratio-dependent predator-prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic stability of the positive steady state does not even guarantee the so-called persistence of the system and, therefore, does not imply global asymptotic stability. It is found that an orbitally asymptotically stable periodic orbit exists in that model. Some sufficient conditions which guarantee the global stability of positive equilibrium are given.     

Nonlinear effects in a discrete-time dynamic model of a stock market

The time evolution of prices and savings in a stock market is modeled by a discrete time nonlinear dynamical system. The model proposed has a unique and unstable steady-state, so that the time evolution is determined by the nonlinear effects acting out of the equilibrium. The nonlinearities strongly influence the kind of long-run dynamics of the system. In particular, the global geometric properties of the noninvertible map of the plane, whose iteration gives the evolution of the system, are important to understand the global bifurcations which change the qualitative properties of the asymptotic dynamics. Such global bifurcations are studied by geometric and numerical methods based on the theory of critical curves, a powerful tool for the characterization of the global dynamical properties of noninvertible mappings of the plane. The model unfolds more complex chaotic and unpredictable trajectories as a consequence of increasing agents' “speculative” or “capital gain realizing” attitudes. The global analysis indicates that, for some ranges of the parameter values, the system has several coexisting attractors, and it may not be robust with respect to exogenous shocks due to the complexity of the basins of attraction.     

Qualitative analysis of a coupled reaction-diffusion model in biology with time delays

Certain biochemical reaction can be modeled by a coupled system of time-delayed ordinary differential equations and linear parabolic partial differential equations. In a three-compartment model these equations are coupled through the boundary conditions. The aim of this paper is to give a qualitive analysis of this unusual coupled system. The analysis includes the existence and uniqueness of a global solution, explicit upper and lower bounds of the solution, and global stability of a steady-state solution. The global stability result is with respect to any nonnegative initial perturbation and is independent of the time delays in the process of reaction. Special attention is given to the Goodwin model for biochemical control of genes by a negative feedback mechanism with time delay and diffusion.     

Delay model of glucose-insulin systems: Global stability and oscillated solutions conditional on delays

Recently P. Palumbo, S. Panunzi and A. De Gaetano analyzed a delay model of the glucose-insulin system. They proved its persistence, the existence of a unique positive equilibrium point, as well as the local stability of this point. In this paper we consider further the uniform persistence of such equilibrium solutions and their global stability. Using the omega limit set of a persistent solution and constructing a full time solution, we also investigate the effect of delays in connection with the behavior of oscillating solutions to the system. The model is shown to admit global stability under certain conditions of the parameters. It is also shown that the model admits slowly oscillating behavior, which demonstrates that the model is physiologically consistent and actually applicable to diabetological research.     

Uniform boundedness and stability of global solutions in a strongly coupled three-species cooperating model

Using the energy estimate and Gagliardo–Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for a strongly coupled reaction–diffusion system are proved. This system is the Shigesada–Kawasaki–Teramoto three-species cooperating model with self- and cross-population pressure. Meanwhile, some criteria on the global asymptotic stability of the positive equilibrium point for the model are also given by Lyapunov function. As a by-product, we proved that only constant steady states exist if the diffusion coefficients are large enough.     

基于Agent与分解协调的综合生产计划研究

以作业单元为局部决策Agent,车间管理者为全局协调Agent,引入生产节点间的内部结算价格,基于多Agent系统,建立了综合生产计划的分布式决策模型.通过将局部Agent决策目标的总和与全局Agent决策目标进行对比,证明了所引入的内部结算价格就是全局Agent目标函数关于物流平衡约束的Lagrange乘子.基于Lagrange分解协调原理,设计了局部作业单元Agent和全局协调Agent的迭代协调算法.该迭代算法以上次计算的中间结果作为对其它作业单元生产需求的估计,从而能将各个生产单元Agent的决策模型分离,实现了分布建模与求解.在算例研究中使用启发式规则来确定Lagrange乘子迭代的步长系数,保证了较好的收敛性,证明模型和算法是有效的.     

一类非最小相位非线性系统的鲁棒输出调节

研究了一类具有非最小相位和非线性外部系统的非线性系统的全局鲁棒输出调节问题.首先,利用浸入系统设计了一个非线性内模.其次,把原系统的全局鲁棒输出调节问题转化为增广系统的全局鲁棒镇定问题.然后,利用改变能量函数和动态增益技巧设计了一个状态反馈控制器,使得闭环系统的解有界并且跟踪误差渐近趋于零.最后,利用仿真结果验证了所设计的控制器的有效性.     

On the differential variational inequalities of parabolic‐elliptic type

We consider a model of infinite dimensional differential variational inequalities formulated by a parabolic differential inclusion and an elliptic variational inequality. The existence of global solution and global attractor for the semiflow governed by our system is proved by using measure of noncompactness. Copyright © 2017 John Wiley & Sons, Ltd.     

一类单时滞线性系统的模糊变结构控制

研究了一类单时滞线性系统变结构控制律的设计方法,基于模糊T-S模型把一类单时滞线性系统化为若干个时滞子系统,然后对时滞子系统设计变结构控制律,取全局控制作为系统的控制律,从而达到对单时滞线性系统系统进行控制的目的,给出了单时滞系统的滑模稳定的条件.仿真表明控制策略的有效性.     

Local Compliance Effects on the Global Pressure-Volume Relationship in Models of Intracranial Pressure Dynamics

The experimentally-measured pressure-volume relationship for the human intracranial system is a nonlinear ‘S-shaped’ curve with two pressure plateaus, a point of inflection, and a vertical asymptote at high pressures where all capacity for volume compensation is lost. In lumped-parameter mathematical models of the intracranial system, local compliance parameters relate volume adjustments to dynamic changes in pressure differences between adjacent model subunits. This work explores the relationship between the forms used for local model compliances and the calculated global pressure-volume relationship. It is shown that the experimentally-measured global relationship can be recovered using physiologically motivated expressions for the local compliances at the interfaces between the venous-cerebrospinal fluid (CSF) subunits and arterial-CSF subunits in the model. Establishment of a consistent link between local model compliances and the physiological bulk pressure-volume relationship is essential if lumped-parameter models are to be capable of realistically predicting intracranial pressure dynamics.     

Global Dynamics of the Oregonator System

In this work, the existence and properties of a global attractor for the solution semiflow of the Oregonator system are proved. The Oregonator system is the mathematical model of the celebrated Belousov–Zhabotinskii reaction. A rescaling and grouping estimation method is developed to show the absorbing property and the asymptotic compactness of the solution trajectories of this three‐component reaction–diffusion system with quadratic nonlinearity. It is also proved that the fractal dimension of the global attractor is finite and an exponential attractor exists for the Oregonator semiflow. Copyright © 2012 John Wiley & Sons, Ltd.     

Global existence for a mathematical model of the immune response to cancer

In this paper we study a mathematical model describing the growth of a solid in the presence of an immune system response. The model is strongly coupled degenerate reaction–diffusion system, in which the equations involve discontinuous terms. By using the approximation method combined with energy estimates and the bootstrap arguments, we prove that this system has a global classical solution.