EXISTENCE RESULTS FOR GLOBALLY EFFICIENT SOLUTIONS OF VECTOR EQUILIBRIUM PROBLEMS VIA A GENERALIZED KKM PRINCIPLE

The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set.

Qualitative Considerations on the Influence of the Gases Water Vapor and Carbon Dioxide on the Global Environmental Temperature from the Point of View of Textbook Knowledge

The solar radiation that hits the Earth conditions the dynamic equilibrium that prevails on our planet. Consideration of basic physical-chemical knowledge shows that this equilibrium can be changed only by additional energy input or prolongation of the interaction time solar radiation—Earth matter. The contribution of H2O(g) and CO2 to the protection of the earth against excessive warming is experimentally and by basic laws of nature secured. For a greenhouse effect, a part of the earth radiation must be radiated back to the earth and then into space. If one understands the earth radiation as radiation of a black body with the average global environmental temperature, from all vibrations normal modes of the gases H2O(g) and CO2 only the bending mode of CO2 with 4% of the solar constant can contribute beside the rotational modes of the water to the greenhouse effect. The contributions of the normal modes of H2O(g) and CO2 to the heat capacity of the atmosphere are negligible. Therefore, in agreement with studies by K. Ångström, CO2 contributes only to the stabilization of the global environmental temperature. Whether the use of renewable energies can actually at least mitigate the increase of the environmental temperature is by no means certain but must be examined for each individual case. With certainty, this goal can only be achieved by reducing the energy consumption of mankind.

手机成瘾动力学模型的定性分析

根据手机用户不同群体之间的人员转移关系,文章构建了一个手机成瘾动力学模型.首先,计算了模型的基本再生数和两个平衡点.其次,证明了在一定条件下,非负平衡点和唯一正平衡点是全局渐近稳定的.最后,用数值算例验证了相关结论的正确性.

弱全局信息下巨星座多路并发熵均衡路由策略

为保障地面系统对巨星座信息的高效获取,考虑实际卫星感知能力的约束,提出一种弱全局信息下巨星座多路并发熵均衡路由策略。首先,根据星座运行模式构建簇群,同时考虑簇的感知能力,建立弱全局信息下的“星-星/星-地”数据传输模型。其次,综合考虑网络结构、数据流量分布和信息多点频发等因素,对现有算法进行改进,引入熵作为评估节点负载分布均匀度的量化指标,引入惩罚因子对路径成本进行动态调整,并通过滚动窗口法规划巨星座多路并发情况下的对地传输路径。最后,以Starlink一期部署的卫星为例,进行数值仿真,验证所提方法的有效性。

新常态下超大型城市干线路网发展思路——以深圳市为例

新常态下,经济增速放缓,传统发展方式难以为继,需要创新动力机制,加强供给侧改革。城市干线路网作为支撑城市空间结构优化调整的主动脉,新阶段,理应聚焦城市发展新趋势,从“高速度增长”向“高质量发展”转变。本文剖析当前深圳干线路网存在的问题,研判未来发展态势,提出未来深圳干线路网应该实现“四大升级”,引导人口、用地、建筑结构同步优化升级,促进区域供给侧的生产要素合理和有序流动,提高资源配置效率和质量,促进区域产业升级和经济发展。

集值向量拟均衡问题的Global近似对偶

在适当条件下,研究集值向量拟均衡问题的Global近似对偶。首先引入了具Global有效性集值向量拟均衡问题及其对偶问题,然后借助于凸集拟内部的概念,讨论了集值向量拟均衡问题的ε-Global有效解与其对偶问题的ε-Global有效解之间的关系,得到了集值向量拟均衡问题的对偶定理。

求解逆混合变分不等式问题的动力系统方法

本文主要研究求解逆混合变分不等式问题的动力系统方法。首先,在强单调和Lipschitz连续性的假设下,通过借助广义f-投影算子的性质,得到逆混合变分不等式问题有唯一解的充分条件。进一步考虑一个动力系统方法来求解逆混合变分不等式问题,而且该动力系统具有唯一均衡点。最后,证明在强单调和Lipschitz连续性的条件下该动力系统的唯一均衡点是全局指数稳定的。

一类先天免疫应答模型的稳定性分析

主要研究了一类关于病原体与中性粒细胞(PMNs)之间的相互作用的免疫应答模型.首先讨论了该模型边界平衡点的存在条件;其次,通过Poincare′变换与中心流形理论证明了该模型边界平衡点的全局渐近稳定性;最后,利用MATLAB软件包对得到的结论进行了适当的数值模拟.

具约束向量拟均衡问题的Global有效解的最优条件

向量均衡问题是运筹学的重要组成部分,其研究的主要内容包含各种解的存在性、稳定性、连续性、连通性、适定性、最优条件。向量均衡问题的解主要有有效解、弱有效解、强有效解、Global有效解、Henig有效解、超有效解。研究向量均衡问题各种有效解的最优条件是向量均衡问题的一个重要课题。首先,在实Hausdorff拓扑线性空间中引入具约束条件的向量拟均衡问题及其Global有效解的概念;其次,在实拓扑线性空间中分析了锥-凸、几乎锥-类凸与几乎锥-次类凸3种广义凸性的内在关系;最后,在3种广义凸性条件下借助于凸集分离定理给出了具约束条件的向量拟均衡问题Global有效解的充要条件。

集值向量拟均衡问题的ε-Global对偶

引入具集值映射的ε-Global向量拟均衡问题及其对偶问题,在广义凸性与广义Slater条件下,讨论ε-Global向量拟均衡问题的ε-Global有效解与其对偶问题的ε-Global有效解之间的关系,得到了ε-Global向量拟均衡问题的对偶定理。

一类高阶有理差分方程解的全局吸引性

为研究一类高阶有理差分方程的动力学性质,利用M&m定理方法来证明该类方程解的全局吸引性,给出了该类方程的正平衡解是全局吸引子的充分条件,并讨论一类高阶有理差分方程具备全局吸引性时参数p,q所满足的条件,最后通过数值计算作出图像验证结论的正确性.

一类非线性差分系统的动力学性质

使用差分系统的动力学理论、Jacobian矩阵以及数值模拟研究了一类非线性差分系统■的解的动力学性质,即有界性、局部渐近稳定性、全局吸引子、全局渐近稳定性等.

GLOBAL ANALYSIS OF SOME EPIDEMIC MODELS WITH GENERAL CONTACT RATE AND CONSTANT IMMIGRATION

An epidemic models of SIR type and SIRS type with general contact rate and constant immigration of each class were discussed by means of theory of limit system and suitable Liapunov functions. In the absence of input of infectious individuals, the threshold of existence of endemic equilibrium is found.For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model, the sufficient and necessary conditions of global asymptotical stabilities are all obtained.For corresponding SIRS model, the sufficient conditions of global asymptotical stabilities of the disease-free equilibrium and the endemic equilibrium are obtained. In the existence of input of infectious individuals, the models have no disease-free equilibrium. For corresponding SIR model, the endemic equilibrium is globally asymptotically stable; for corresponding SIRS model, the sufficient conditions of global asymptotical stability of the endemic equilibrium are obtained.

GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION

In this paper the global attractivity of the nonlinear difference equationis investigated, where a,b, A ∈ (0,∞), k is an positive integer and the initial conditions x- k, …, x-1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].

On global behavior of the system of rational difference equations x_(n+1)=p+y_(n-k)/x_n,y_(n+1)=q+x_(n-k)/y_n

In this paper,we investigate the boundedness character,the global attractivity and the periodic nature of the system of rational difference equations:x=p+y/x,y=q+x/y,n=0,1,2…,where p>0,q>0,k∈{1,2,…} and the initial values xi,yi∈(0,∞),i=-k,-k+1,…,0. Some new results are obtained.

Global asymptotic stability for Hopfield-type neural networks with diffusion effects

The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.

Global exponential stability of Cohen-Grossberg neural networks with variable delays

A class of generalized Cohen-Grossberg neural networks（CGNNs） with variable de- lays are investigated. By introducing a new type of Lyapunov functional and applying the homeomorphism theory and inequality technique, some new conditions axe derived ensuring the existence and uniqueness of the equilibrium point and its global exponential stability for CGNNs. These results obtained are independent of delays, develop the existent outcome in the earlier literature and are very easily checked in practice.

Fuzzy Global Stability Analysis of the Dynamics of Malaria with Fuzzy Transmission and Recovery Rates

In this paper, fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (), we reach the model disease-free equilibrium. Using Choquet integral, the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible, Exposed, Infected, Recovered, susceptible-Susceptible, Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium is globally asymptotically stable if or if the basic reproduction number is less than one (). When and , there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set . Finally, the numerical simulation has been done for showing the effectiveness of our analytical results.

Global Analysis of an SEIR Epidemic Model with a Ratio-Dependent Nonlinear Incidence Rate

In this paper, a SEIR model with ratio-dependent transmission rate in the form ?is studied and the basic reproduction number which determines the disease’s extinction or continued existence is obtained. By constructing the proper Lyapunov function, we prove that if R0 ≤ 1, the disease-free equilibrium point of the model is globally asymptotically stable and the disease always dies out;if R0 > 1, the endemic equilibrium point is globally asymptotically stable and the disease persists.

Global Stability of a SVEIR Epidemic Model: Application to Poliomyelitis Transmission Dynamics

The lack of treatment for poliomyelitis doing that only means of preventing is immunization with live oral polio vaccine (OPV) or/and inactivated polio vaccine (IPV). Poliomyelitis is a very contagious viral infection caused by poliovirus. Children are principally attacked. In this paper, we assess the impact of vaccination in the control of spread of poliomyelitis via a deterministic SVEIR (Susceptible-Vaccinated-Latent-Infectious-Removed) model of infectious disease transmission, where vaccinated individuals are also susceptible, although to a lesser degree. Using Lyapunov-Lasalle methods, we prove the global asymptotic stability of the unique endemic equilibrium whenever ?. Numerical simulations, using poliomyelitis data from Cameroon, are conducted to approve analytic results and to show the importance of vaccinate coverage in the control of disease spread.