On Lossless Reciprocal and Nonreciprocal Matching Networks of an Active Load

A general matching theory between an arbitrary passive impedance and an active load impedance is presented. It extends the broadband matching theory to include both lossless reciprocal and nonreciprocal networks. Application of the result to the design of nonreciprocal negative-resistance amplifier is given. The significance of the present approach is that the realization of the equalizer is accomplished by means of the driving-point synthesis based on the Darlington theory. The result enlarges the domain of realizable broadband matching networks.An illustrative example is presented to show the design procedure and the conditions under which a lossless nonreciprocal network is realized for an active load.     

Exact Model-Matching of 2-D Systems via State Feedback

This paper considers the problem of matching the transfer function matrix of a given two-dimensional (2-D) system to that of a desired 2-D model using state feedback. The approach followed refers to systems having square transfer function matrices and reduces the problem to that of solving a linear system of equations. Furthermore, necessary and sufficient conditions are established for exact matching. An example is included to illustrate the proposed method.     

Tracking community evolution in social networks: A survey

This paper presents a survey of previous studies done on the problem of tracking community evolution over time in dynamic social networks. This problem is of crucial importance in the field of social network analysis. The goal of our paper is to classify existing methods dealing with the issue. We propose a classification of various methods for tracking community evolution in dynamic social networks into four main approaches using as a criterion the functioning principle: the first one is based on independent successive static detection and matching; the second is based on dependent successive static detection; the third is based on simultaneous study of all stages of community evolution; finally, the fourth and last one concerns methods working directly on temporal networks. Our paper starts by giving basic concepts about social networks, community structure and strategies for evaluating community detection methods. Then, it describes the different approaches, and exposes the strengths as well as the weaknesses of each.     

Cascading state-space decomposition of Boolean control networks by nested method

Boolean control networks are a kind of discrete logical dynamical systems. They are recently attracting considerable interest as computational models for genetic and cellular networks. In this paper, we investigate the cascading state-space decomposition problem for Boolean control networks by nested method. Firstly, based on the semi-tensor product of matrices, we obtain some algebraic conditions for the cascading state-space decomposition. Secondly, the multi-layer nested block matrix is defined, and two necessary and sufficient conditions are put forward based on this kind of matrices. Besides, a method is given to design controllers. Finally, an example is given to display the effectiveness of the method provided in this paper.     

Mean-square pinning control of fractional stochastic discrete-time complex networks

This paper considers the mean-square pinning control problem of fractional stochastic discrete-time complex networks. First, a new fractional stochastic discrete-time complex networks model with stochastic noise is established. Then, some pinning controllers and sufficient conditions are developed for the complex networks. By adopting Lyapunov energy function theory and matrix analysis theory, it proved that the synchronization of the fractional stochastic discrete-time complex networks can be achieved in a mean-square sense via pinning control. In addition, these results are extended to solve the synchronization problem of general fractional discrete-time complex networks without noise. Finally, several numerical examples are given to verify the correctness of the obtained theoretical results.     

Dissipativity of discrete-time BAM stochastic neural networks with Markovian switching and impulses

This paper addresses the problem of global exponential dissipativity for a class of uncertain discrete-time BAM stochastic neural networks with time-varying delays, Markovian jumping and impulses. By constructing a proper Lyapunov–Krasovskii functional and combining with linear matrix inequality (LMI) technique, several sufficient conditions are derived for verifying the global exponential dissipativity in the mean square of such stochastic discrete-time BAM neural networks. The derived conditions are established in terms of linear matrix inequalities, which can be easily solved by some available software packages. One important feature presented in our paper is that without employing model transformation and free-weighting matrices our obtained result leads to less conservatism. Additionally, three numerical examples with simulation results are provided to show the effectiveness and usefulness of the obtained result.     

Optimal control of singular boolean control networks via Ledley solution method

This paper investigates the optimal control problem for a class of Boolean control networks, called singular Boolean control networks (SBCNs), which consist of two parts: difference equations and algebraic equations. By constructing the truth matrix of Ledley solution, necessary and sufficient conditions are provided for the solvability of SBNs (or SBCNs). Then an effective algorithm is presented to design an optimal control sequence by using the controllability matrix of normalized Boolean control networks.     

Synthesis of biquadratic impedances with at most four passive elements

In this paper, we consider the passive network synthesis problem of biquadratic impedances with at most four elements, motivated by the passive mechanical control. In order to solve this problem, a necessary and sufficient realizability condition for no more than three elements is obtained by some topological properties derived previously. Furthermore, the constraints on the possible realizations are used to derive the networks which can cover all the cases, and they are classified as several quartets. Through investigating one of the networks in each quartet, we obtain a necessary and sufficient condition for any biquadratic impedance to be realizable with at most four elements. Finally, the interlocking conditions are illustrated graphically, and numerical examples are given.     

Global dissipativity of delayed neural networks with impulses

In this paper, we investigate the problem of global exponential dissipativity of neural networks with variable delays and impulses. The impulses are classified into three classes: input disturbances, stabilizing and “neutral” type—the impulses are neither helpful for stabilizing nor destabilizing the neural networks. We handle the three types of impulses in a uniform way by using the excellent ideology introduced recently. To this end, we propose new techniques which coupled with more general Lyapunov functions to realize the ideology and it is shown that they are more effective. Exponential dissipativity conditions are established in terms of linear matrix inequalities (LMIs) and these conditions can be straightforwardly reduced to exponential stability conditions. Numerical results are given to show that the obtained conditions are effective and less conservative than the existing ones.     

Steady-state analysis of probabilistic Boolean networks

This paper investigates steady-state distributions of probabilistic Boolean networks via cascading aggregation. Under this approach, the problem is converted to computing least square solutions to several corresponding equations. Two necessary and sufficient conditions for the existence of the steady-state distributions for probabilistic Boolean networks are given firstly. Secondly, an algorithm for finding the steady-state distributions of probabilistic probabilistic Boolean networks is given. Finally, a numerical example is given to show the effectiveness of the proposed method.     

Finite-time stochastic stabilization for BAM neural networks with uncertainties

This paper is concerned with the finite-time stabilization for a class of stochastic BAM neural networks with parameter uncertainties. Compared with the previous references, a continuous stabilizator is designed for stabilizing the states of stochastic BAM neural networks in finite time. Based on the finite-time stability theorem of stochastic nonlinear systems, several sufficient conditions are proposed for guaranteeing the finite-time stability of the controlled neural networks in probability. Meanwhile, the gains of the finite-time controller could be designed by solving some linear matrix inequalities. Furthermore, for the stochastic BAM neural networks with uncertain parameters, the problem of robust finite-time stabilization could also be ensured as well. Finally, two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.     

Discrete-time stochastic impulsive BAM neural networks with leakage and mixed time delays: An exponential stability problem

In this paper, the stability analysis of impulsive discrete-time stochastic BAM neural networks with leakage and mixed time delays is investigated via some novel Lyapunov–Krasoviskii functional terms and effective techniques. For the target model, stochastic disturbances are described by Brownian motion. Then the result is further extended to address the problem of robust stability of uncertain discrete-time BAM neural networks. The conditions obtained here are expressed in terms of Linear Matrix Inequalities (LMIs), which can be easily checked by MATLAB LMI control toolbox. Finally, few numerical examples are presented to substantiate the effectiveness of the derived LMI-based stability conditions.     

Adaptive output-feedback control for nonlinear time-delay systems in pure-feedback form

The main contribution of this paper is to develop an adaptive output-feedback control approach for a class of uncertain nonlinear systems with unknown time-varying delays in the pure-feedback form. Both the non-affine nonlinear functions and the unknown time-varying delayed functions related to all state variables are considered. These conditions make the controller design difficult and challenging because the output-feedback controller should be designed using only the output information. In order to overcome these conditions, we design an observer-based adaptive dynamic surface controller where the time-delay effects are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique using neural networks. A first-order filter is added to the control input to avoid the algebraic loop problem caused by the non-affine structure. It is proved that all the signals in the closed-loop system are semi-globally uniformly bounded and the tracking error converges to an adjustable neighborhood of the origin.     

Improved approaches to stability criteria for neural networks with time-varying delays

In this paper, the problem of stability analysis for neural networks with time-varying delays is considered. By the use of a newly augmented Lyapunov functional and some novel techniques, sufficient conditions to guarantee the asymptotic stability of the concerned networks are established in terms of linear matrix inequalities (LMIs). Three numerical examples are given to show the improved stability region of the proposed works.     

A modified Lyapunov functional with application to stability of neutral-type neural networks with time delays

This paper investigates the problem for stability of neutral-type dynamical neural networks involving delay parameters. Different form the previously reported results, the states of the neurons involve multiple delays and time derivative of states of neurons include discrete time delays. The stability of such neural systems has not been given much attention in the past literature due to the difficulty of finding Lyapunov functionals which are suitable for stability analysis of this type of neural networks. This paper constructs a generalized Lyapunov functional by introducing new terms into the well-known Lyapunov functional that enables us to conduct a theoretical investigation into stability analysis of delayed neutral-type neural systems. Based on this modified novel Lyapunov functional, sufficient criteria are derived, which guarantee the existence, uniqueness and global asymptotic stability of the equilibrium point of the neutral-type neural networks with multiple delays in the states and discrete delays in the time derivative of the states. The applicability of the proposed stability conditions rely on testing two basic matrix properties. The constraints impose on the system matrices are determined by using nonsingular M-matrix condition, and the constraints imposed on the coefficients of the time derivative of the delayed state variables are derived by exploiting the vector-matrix norms. We also note that the obtained stability conditions have no involvement with the delay parameters and expressed in terms of nonlinear Lipschitz activation functions. We present a constructive numerical example for this class of neural networks to give a systematic procedure for determining the imposed conditions on the whole system parameters of the delayed neutral-type neural systems.     

Average consensus in networks of dynamic agents with uncertain topologies and time-varying delays

In this paper, we study average consensus problem in networks of dynamic agents with uncertain topologies as well as time-varying communication delays. By using the linear matrix inequality method, we establish several sufficient conditions for average consensus in the existence of both uncertainties and delays. Several linear matrix inequality conditions are presented to determine the allowable upper bounds of time-varying communication delays and uncertainties. Numerical examples are worked out to illustrate the theoretical results.     

全球商品贸易网络生长特征及动力机制

经济全球化时代,国家间商品流动频繁,商品贸易网络化特征突出,亟需从关系网络的生长逻辑探究全球商品贸易的互动场景与演进机理。本文基于1996—2016年全球商品贸易流量数据,借助社会网络分析方法和ArcGIS可视化工具揭示了全球商品贸易网络的生长过程,运用指数随机图模型分析了全球商品贸易网络生长的动力机制。结果表明：①全球商品贸易网络呈扩张式生长,逐步形成“三核”互联主导的“大三角”空间结构,网络骨架的三大集群凸显。中国主导的集群大幅拓展,美国和德国主导的集群日益收缩。各国家（地区）在网络中的分工明确,网络功能差异显著并表现出不同变化特征。②全球商品贸易网络生长受自组织性、国家（地区）匹配性、国家（地区）集散性等内生动力和外生网络嵌入性等外在推力的共同驱动。其中,互惠关系是自组织性的主要结构,国家（地区）收入水平、市场开放趋同性和制度环境异质性是匹配性的关键因素,经济优势和产业竞争力是集散性的重要基础,殖民历史网络、留学生交流网络、语言同构网络、论文合作网络是重要的外生网络。传统的比较优势理论仍然适用于全球商品贸易网络生长机理的解释,尤其对国家（地区）匹配性和集散性的解释力更强。     

Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques

A general system of the time-dependent partial differential equations containing several arbitrary initial and boundary conditions is considered. A hybrid method based on artificial neural networks, minimization techniques and collocation methods is proposed to determine a related approximate solution in a closed analytical form. The optimal values for the corresponding adjustable parameters are calculated. An accurate approximate solution is obtained, that works well for interior and exterior points of the original domain. Numerical efficiency and accuracy of the hybrid method are investigated by two-test problems including an initial value and a boundary value problem for the two-dimensional biharmonic equation.     

Finite-time synchronization of delayed dynamical networks via aperiodically intermittent control

In this paper, we concern the finite-time synchronization problem for delayed dynamical networks via aperiodically intermittent control. Compared with some correspondingly previous results, the intermittent control can be aperiodic which is more general. Moreover, by establishing a new differential inequality and constructing Lyapunov function, several useful criteria are derived analytically to realize finite-time synchronization for delay complex networks. Additionally, as a special case, some sufficient conditions ensuring the finite-time synchronization for a class of coupled neural network are obtained. It is worth noting that the convergence time is carefully discussed and does not depend on control widths or rest widths for the proposed aperiodically intermittent control. Finally, a numerical example is given to demonstrate the validness of the proposed scheme.