Analysis of global exponential stability for a class of bi—directional associative memory networks

In real-time applications of bi-directional associative memory (BAM) networks.a global exponentially stable equilibrium is highly desired.The existence,uniqueness and global exponential stability for a class of BAM networks are studied in this paper,the signal function of neurons is assumed to be piece-wise linear from the engineering point of view.A very concise condition for the equilbrium of such a network being globally exponentially stable is derived.which makes the pactical design of this kind of networks an easy job.     

Network-Based Driving Force of National Economic Development: A Social Capital Perspective

Network science has been widely applied in theoretical and empirical studies of global value chain (GVC), and many related articles have emerged, forming many more mature and complete analytical frameworks. Among them, the GVC accounting method based on complex network theory is different from the mainstream economics in both research angle and content. In this paper, we build up global industrial value chain network (GIVCN) models based on World Input–Output Database, introduce the theoretical framework of Social Capital, and define the network-based indicators with economic meanings. Second, we follow the econometric framework to analyze the hypothesis and test whether it is true. Finally, we study how the three types of capital constituted by these indicators interact with each other, and discuss their impact on the social capital (economic development level, i.e., GDP). The results prove that the structural capital (industrial status) has a positive impact on the social capital; the relational capital (industrial correlation) has a positive impact on both social capital and structural capital; the cognitive capital (industrial structure) has a small impact on the social capital, structural capital, and relational capital.     

Structure and response in the world trade network

We examine how the structure of the world trade network has been shaped by globalization and recessions over the last 40?years. We show that by treating the world trade network as an evolving system, theory predicts the trade network is more sensitive to recessionary shocks and recovers more slowly from them now than it did 40?years ago, due to structural changes in the world trade network induced by globalization. We also show that recession-induced change to the world trade network leads to an increased hierarchical structure of the global trade network for a few years after the recession.     

Research on spatial economic structure for different economic sectors from a perspective of a complex network

The economy system is a complex system, and the complex network is a powerful tool to study its complexity. Here we calculate the economic distance matrices based on annual GDP of nine economic sectors from 1995–2010 in 31 Chinese provinces and autonomous regions,¹ then build several spatial economic networks through the threshold method and the Minimal Spanning Tree method. After the analysis on the structure of the networks and the influence of geographic distance, some conclusions are drawn. First, connectivity distribution of a spatial economic network does not follow the power law. Second, according to the network structure, nine economic sectors could be divided into two groups, and there is significant discrepancy of network structure between these two groups. Moreover, the influence of the geographic distance plays an important role on the structure of a spatial economic network, network parameters are changed with the influence of the geographic distance. At last, 2000 km is the critical value for geographic distance: for real estate and finance, the spearman’s rho with l<2000$l<2000$ is bigger than that with l>2000$l>2000$, and the case is opposite for other economic sectors.     

Distributions of positive correlations in sectoral value added growth in the global economic network*

International trade has grown considerably during the process of globalization. Complex supply chains for the production of goods have resulted in an increasingly connected International Trade Network (ITN). Traditionally, direct trade relations between industries have been regarded as mediators of supply and demand spillovers. With increasing network connectivity the question arises if higher-order relations become more important in explaining a national sector’s susceptibility to supply and demand changes of its trading partner. In this study we address this question by investigating empirically to what extent the topological properties of the ITN provide information about positive correlations in the production of two industry sectors. We observe that although direct trade relations between industries serve as important indicators for correlations in the industries’ value added growth, opportunities of substitution for required production inputs as well as second-order trade relations cannot be neglected. Our results contribute to a better understanding of the relation between trade and economic productivity and can serve as a basis for the improvement of crisis spreading models that evaluate contagion threats in the case of a node’s failure in the ITN.     

Optimal vaccination and treatment of an epidemic network model

In this Letter, we firstly propose an epidemic network model incorporating two controls which are vaccination and treatment. For the constant controls, by using Lyapunov function, global stability of the disease-free equilibrium and the endemic equilibrium of the model is investigated. For the non-constant controls, by using the optimal control strategy, we discuss an optimal strategy to minimize the total number of the infected and the cost associated with vaccination and treatment. Table 1 and Figs. 1–5 are presented to show the global stability and the efficiency of this optimal control.     

Investigation of major international and Turkish companies via hierarchical methods and bootstrap approach

We present a study, within the scope of econophysics, of the hierarchical structure of 98 among the largest international companies including 18 among the largest Turkish companies, namely Banks, Automobile, Software-hardware, Telecommunication Services, Energy and the Oil-Gas sectors, viewed as a network of interacting companies. We analyze the daily time series data of the Boerse-Frankfurt and Istanbul Stock Exchange. We examine the topological properties among the companies over the period 2006–2010 by using the concept of hierarchical structure methods (the minimal spanning tree (MST) and the hierarchical tree (HT)). The period is divided into three subperiods, namely 2006–2007, 2008 which was the year of global economic crisis, and 2009–2010, in order to test various time-windows and observe temporal evolution. We carry out bootstrap analyses to associate the value of statistical reliability to the links of the MSTs and HTs. We also use average linkage clustering analysis (ALCA) in order to better observe the cluster structure. From these studies, we find that the interactions among the Banks/Energy sectors and the other sectors were reduced after the global economic crisis; hence the effects of the Banks and Energy sectors on the correlations of all companies were decreased. Telecommunication Services were also greatly affected by the crisis. We also observed that the Automobile and Banks sectors, including Turkish companies as well as some companies from the USA, Japan and Germany were strongly correlated with each other in all periods.     

Simple nonlinear systems and navigating catastrophes

Tipping points are a common occurrence in complex adaptive systems. In such systemsfeedback dynamics strongly influence equilibrium points and they are one of the principalconcerns of research in this area. Tipping points occur as small changes in systemparameters result in disproportionately large changes in the global properties of thesystem. In order to show how tipping points might be managed we use the Maximum Entropy(MaxEnt) method developed by Jaynes to find the fixed points of an economic system in twodifferent ways. In the first, economic agents optimise their choices based solely on theirpersonal benefits. In the second they optimise the total benefits of the system, takinginto account the effects of all agent’s actions. The effect is to move the game from arecently introduced dual localised Lagrangian problem to that of a singleglobal Lagrangian. This leads to two distinctly different but relatedsolutions where localised optimisation provides more flexibility than global optimisation.This added flexibility allows an economic system to be managed by adjusting therelationship between macro parameters, in this sense such manipulations provide for thepossibility of “steering” an economy around potential disasters.     

The Local Structure of Globalization

We study the evolution of the network of foreign direct investment (FDI) in the international electricity industry during the period 1994–2003. We assume that the ties in the network of investment relations between countries are created and deleted in continuous time, according to a conditional Gibbs distribution. This assumption allows us to take simultaneously into account the aggregate predictions of the well-established gravity model of international trade as well as local dependencies between network ties connecting the countries in our sample. According to the modified version of the gravity model that we specify, the probability of observing an investment tie between two countries depends on the mass of the economies involved, their physical distance, and the tendency of the network to self-organize into local configurations of network ties. While the limiting distribution of the data generating process is an exponential random graph model, we do not assume the system to be in equilibrium. We find evidence of the effects of the standard gravity model of international trade on evolution of the global FDI network. However, we also provide evidence of significant dyadic and extra-dyadic dependencies between investment ties that are typically ignored in available research. We show that local dependencies between national electricity industries are sufficient for explaining global properties of the network of foreign direct investments. We also show, however, that network dependencies vary significantly over time giving rise to a time-heterogeneous localized process of network evolution.     

Global dynamics of a novel multi-group model for computer worms

In this paper, we study worm dynamics in computer networks composed of many autonomous systems. A novel multigroup SIQR (susceptible-infected-quarantined-removed) model is proposed for computer worms by explicitly considering anti-virus measures and the network infrastructure. Then, the basic reproduction number of worm R0 is derived and the global dynamics of the model are established. It is shown that if R0 is less than or equal to 1, the disease-free equilibrium is globally asymptotically stable and the worm dies out eventually, whereas, if R0 is greater than 1, one unique endemic equilibrium exists and it is globally asymptotically stable, thus the worm persists in the network. Finally, numerical simulations are given to illustrate the theoretical results.     

Entropy and equilibrium state of free market models

Many recent models of trade dynamics use the simple idea of wealth exchanges among economic agents in order to obtain a stable or equilibrium distribution of wealth among the agents. In particular, a plain analogy compares the wealth in a society with the energy in a physical system, and the trade between agents to the energy exchange between molecules during collisions. In physical systems, the energy exchange among molecules leads to a state of equipartition of the energy and to an equilibrium situation where the entropy is a maximum. On the other hand, in a large class of exchange models, the system converges to a very unequal condensed state, where one or a few agents concentrate all the wealth of the society while the wide majority of agents shares zero or almost zero fraction of the wealth. So, in those economic systems a minimum entropy state is attained. We propose here an analytical model where we investigate the effects of a particular class of economic exchanges that minimize the entropy. By solving the model we discuss the conditions that can drive the system to a state of minimum entropy, as well as the mechanisms to recover a kind of equipartition of wealth.     

自适应网络中病毒传播的稳定性和分岔行为研究

自适应复杂网络是以节点状态与拓扑结构之间存在反馈回路为特征的网络. 针对自适应网络病毒传播模型, 利用非线性微分动力学系统研究病毒传播行为; 通过分析非线性系统对应雅可比矩阵的特征方程, 研究其平衡点的局部稳定性和分岔行为, 并推导出各种分岔点的计算公式. 研究表明, 当病毒传播阈值小于病毒存在阈值, 即R₀0^c时, 网络中病毒逐渐消除, 系统的无病毒平衡点是局部渐近稳定的; R₀^c0<1时, 网络出现滞后分岔, 产生双稳态现象, 系统存在稳定的无病毒平衡点、较大稳定的地方病平衡点和较小不稳定的地方病平衡点; R₀>1时, 网络中病毒持续存在, 系统唯一的地方病平衡点是局部渐近稳定的. 研究发现, 系统先后出现了鞍结分岔、跨临界分岔、霍普夫分岔等分岔行为. 最后通过数值仿真验证所得结论的正确性. 关键词： 自适应网络 稳定性 分岔 基本再生数     

Spatial price dynamics: From complex network perspective

The spatial price problem means that if the supply price plus the transportation cost is less than the demand price, there exists a trade. Thus, after an amount of exchange, the demand price will decrease. This process is continuous until an equilibrium state is obtained. However, how the trade network structure affects this process has received little attention. In this paper, we give a evolving model to describe the levels of spatial price on different complex network structures. The simulation results show that the network with shorter path length is sensitive to the variation of prices.     

Global stabilization of a Lorenz system

In this paper,using feedback linearizing technique,we show that a Lorenz system can be considered as a cascade system.Moreover,this system satisfies the assumptions of global stabilization of casecade systems.Thus coninuous state feedback control laws are proposed to globally stabilize the Lorenz system at the equilibrium point.Simulation results are presented to verify our method.This method can be further generalized to other chaotic systems such as Chen system,coupled dynamos system,etc.     

Multistability of twisted states in non-locally coupled Kuramoto-type models

A ring of N identical phase oscillators with interactions between L-nearest neighbors is considered, where L ranges from 1 (local coupling) to N/2 (global coupling). The coupling function is a simple sinusoid, as in the Kuramoto model, but with a minus sign which has a profound influence on its behavior. Without the limitation of the generality, the frequency of the free-running oscillators can be set to zero. The resulting system is of gradient type, and therefore, all its solutions converge to an equilibrium point. All so-called q-twisted states, where the phase difference between neighboring oscillators on the ring is 2πq/N, are equilibrium points, where q is an integer. Their stability in the limit N → ∞ is discussed along the line of Wiley et al. [Chaos 16, 015103 (2006)] In addition, we prove that when a twisted state is asymptotically stable for the infinite system, it is also asymptotically stable for sufficiently large N. Note that for smaller N, the same q-twisted states may become unstable and other q-twisted states may become stable. Finally, the existence of additional equilibrium states, called here multi-twisted states, is shown by numerical simulation. The phase difference between neighboring oscillators is approximately 2πq/N in one sector of the ring, -2πq/N in another sector, and it has intermediate values between the two sectors. Our numerical investigation suggests that the number of different stable multi-twisted states grows exponentially as N → ∞. It is possible to interpret the equilibrium points of the coupled phase oscillator network as trajectories of a discrete-time translational dynamical system where the space-variable (position on the ring) plays the role of time. The q-twisted states are then fixed points, and the multi-twisted states are periodic solutions of period N that are close to a heteroclinic cycle. Due to the apparently exponentially fast growing number of such stable periodic solutions, the system shows spatial chaos as N → ∞.     

时滞递归神经网络中神经抑制的作用

研究了具有时滞的二阶递归神经网络中抑制自连接的作用，给出了时滞依赖的全局渐近稳定的充分判据.研究结果表明：抑制自连接可镇定不稳定的网络并使其渐近稳定；抑制自连接的镇定作用受到网络传输时滞的制约.仿真示例验证了结果的有效性. 关键词： 递归神经网络 时滞 抑制神经元 动态行为     

A predator–prey model with diseases in both prey and predator

In this paper, we present and analyze a predator–prey model, in which both predator and prey can be infected. Each of the predator and prey is divided into two categories, susceptible and infected. The epidemics cannot be transmitted between prey and predator by predation. The predation ability of susceptible predators is stronger than infected ones. Likewise, it is more difficult to catch a susceptible prey than an infected one. And the diseases cannot be hereditary in both of the predator and prey populations. Based on the assumptions above, we find that there are six equilibrium points in this model. Using the base reproduction number, we discuss the stability of the equilibrium points qualitatively. Then both of the local and global stabilities of the equilibrium points are analyzed quantitatively by mathematical methods. We provide numerical results to discuss some interesting biological cases that our model exhibits. Lastly, we discuss how the infectious rates affect the stability, and how the other parameters work in the five possible cases within this model.     

An analysis of global robust stability of neural networks with discrete time delays

This Letter presents a new sufficient condition for the existence, uniqueness and global robust asymptotic stability of the equilibrium point for neural networks with discrete time delays. The obtained condition can be easily verified as it is in terms of the network parameters only. Some numerical examples are given to compare our results with previous robust stability results derived in the literature.     

时滞双向联想记忆神经网络的全局稳定性

通过构造一个合适的Lyapunov泛函及应用不等式的分析技巧研究了具有时滞的双向联想记忆 神经网络的平衡点的全局稳定性问题-在对神经元激励函数较宽松的假设条件下（可以不满 足Lipschitz条件），获得了一个新的保证全局渐近稳定性的判定准则-结果可应用于包含非 Lipschitz的一类更加广泛的神经元激励函数的神经网络的设计中- 关键词： Lyapunov泛函 时滞 双向联想记忆神经网络 全局渐近稳定性