Modeling Topology and Nonlinear Dynamical Behavior of the Weighted Scale-Free Networks

An improved weighted scale-free network, which has two evolution mechanisms： topological growth and strength dynamics, has been introduced. The topology structure of the model will be explored in details in this work. The evolution driven mechanism of Olami-Feder Christensen （OFC） model is added to our model to study the self-organlzed criticality and the dynamical behavior. We also.consider attack mechanism and the study of the model with attack is also investigated in this paper. We tlnd there are differences between the model with attack and without attack.     

Modeling Topology and Nonlinear Dynamical Behavior of the Weighted Scale-Free Networks

An improved weighted scale-free network, which has two evolution mechanisms: topological growth and strength dynamics, has been introduced. The topology structure of the model will be explored in details in this work. The evolution driven mechanism of Olami-Feder-Christensen (OFC) model is added to our model to study the self-organized criticality and the dynamical behavior. We also consider attack mechanism and the study of the model with attack is also investigated in this paper. We find there are differences between the model with attack and without attack.     

Scale-Free Properties in Traffic System

In this work, we propose a new model of evolution networks, which is based on the evolution of the traffic flow. In our method, the network growth does not take into account preferential attachment, and the attachment of new node is independent of the degree of nodes. Our aim is that employing the theory of evolution network, we give a further understanding about the dynamical evolution of the traffic flow. We investigate the probability distributions and scaling properties of the proposed model. The simulation results indicate that in the proposed model, the distribution of the output connections can be well described by scale-free distribution. Moreover, the distribution of the connections is largely related to the traffic flow states, such as the exponential distribution (i.e., the scale-free distribution) and random distribution etc.     

Trajectory Control of Scale-Free Dynamical Networks with Exogenous Disturbances

In this paper, the trajectory control of multi-agent dynamical systems with exogenous disturbances is studied. Suppose multiple agents composing of a scale-free network topology, the performance of rejecting disturbances for the low degree node and high degree node is analyzed. Firstly, the consensus of multi-agent systems without disturbances is studied by designing a pinning control strategy on a part of agents, where this pinning control can bring multiple agents' states to an expected consensus track. Then, theinfluence of the disturbances is considered by developing disturbance observers, and disturbance observers based control (DOBC) are developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi-agent systems with disturbances under the composite controller can be achieved for scale-free network topology. Finally, by analyzing examples of multi-agent systems with scale-free network topology and exogenous disturbances, the verities of the results are proved. Under the DOBC with the designed parameters, the trajectory convergence of multi-agent systems is researched by pinning two class of the nodes. We have found that it has more stronger robustness to exogenous disturbances for the high degree node pinned than that of the lowdegree node pinned.     

Dynamical Consensus Algorithm for Second-Order Multi-Agent Systems Subjected to Communication Delay

To solve the dynamical consensus problem of second-order multi-agent systems with communication delay,delay-dependent compensations are added into the normal asynchronously-coupled consensus algorithm so as to make the agents achieve a dynamical consensus. Based on frequency-domain analysis, sufficient conditions are gained for second-order multi-agent systems with communication delay under leaderless and leader-following consensus algorithms respectively. Simulation illustrates the correctness of the results.     

Robust Consensus of Multi-Agent Systems with Uncertain Exogenous Disturbances

The objective of this paper is to investigate the consensus of the multi-agent systems with nonlinear coupling function and external disturbances. The disturbance includes two parts, one part is supposed to be generated by an exogenous system, which is not required to be neutrally stable as in the output
regulation theory, the other part is the modeling uncertainty in the exogenous disturbance system. A novel composite disturbance observer based control (DOBC) and H_∝ control scheme is presented so that the disturbance with the exogenous system can be estimated and compensated and the consensus of the multi-agent systems with fixed and switching graph can be reached by using H_∝ control law. Simulations demonstrate the advantages of the proposed DOBC and H_∝ control scheme.     

Influence of Blurred Ways on Pattern Recognition of a Scale-Free Hopfield Neural Network

We investigate the influence of blurred ways on pattern recognition of a Barabasi-Albert scale-free Hopfield neural network （SFHN） with a small amount of errors. Pattern recognition is an important function of information processing in brain. Due to heterogeneous degree of scale-free network, different blurred ways have different influences on pattern recognition with same errors. Simulation shows that among partial recognition, the larger loading ratio （the number of patterns to average degree P/ （k） ） is, the smaller the overlap of SFHN is. The influence of directed （large） way is largest and the directed （small） way is smallest while random way is intermediate between them. Under the ratio of the numbers of stored patterns to the size of the network PIN is less than O. 1 conditions, there are three families curves of the overlap corresponding to directed （small）, random and directed （large） blurred ways of patterns and these curves are not associated with the size of network and the number of patterns. This phenomenon only occurs in the SFHN. These conclusions are benefit for understanding the relation between neural network structure and brain function.     

Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws

We consider a recently introduced generalization of the Ising model in which individual spin strength can vary. The model is intended for analysis of ordering in systems comprising agents which, although matching in their binarity (i.e., maintaining the iconic Ising features of ‘+’ or ‘−’, ‘up’ or ‘down’, ‘yes’ or ‘no’), differ in their strength. To investigate the interplay between variable properties of nodes and interactions between them, we study the model on a complex network where both the spin strength and degree distributions are governed by power laws. We show that in the annealed network approximation, thermodynamic functions of the model are self-averaging and we obtain an exact solution for the partition function. This allows us derive the leading temperature and field dependencies of thermodynamic functions, their critical behavior, and logarithmic corrections at the interface of different phases. We find the delicate interplay of the two power laws leads to new universality classes.     

Cluster-Delay Mean Square Consensus of Stochastic Multi-Agent Systems with Impulse Time Windows

This paper investigates the cluster-delay mean square consensus problem of a class of first-order nonlinear stochastic multi-agent systems with impulse time windows. Specifically, on the one hand, we have applied a discrete control mechanism (i.e., impulsive control) into the system instead of a continuous one, which has the advantages of low control cost, high convergence speed; on the other hand, we considered the existence of impulse time windows when modeling the system, that is, a single impulse appears randomly within a time window rather than an ideal fixed position. In addition, this paper also considers the influence of stochastic disturbances caused by fluctuations in the external environment. Then, based on algebraic graph theory and Lyapunov stability theory, some sufficiency conditions that the system must meet to reach the consensus state are given. Finally, we designed a simulation example to verify the feasibility of the obtained results.     

Enhancement of scale-free network attack tolerance

Despite the large size of most communication and transportation systems,there are short paths between nodes in these networks which guarantee the efficient information,data and passenger delivery;furthermore these networks have a surprising tolerance under random errors thanks to their inherent scale-free topology.However,their scale-free topology also makes them fragile under intentional attacks,leaving us a challenge on how to improve the network robustness against intentional attacks without losing their strong tolerance under random errors and high message and passenger delivering capacity.Here we propose two methods (SL method and SH method) to enhance scale-free network’s tolerance under attack in different conditions.     

同时考虑传染媒介和传播延迟的复杂网络病毒传播行为研究

提出一种新的流行病传播模型,基于平均场理论,研究传染媒介和传播延迟同时存在对网络中流行病传播行为的影响.理论分析和仿真结果表明,传染媒介和传播延迟同时存在显著增强了网络中流行病爆发的危险性,并加速了流行病的传播.研究还发现,对于给定的有效传播率,均匀网络中流行病的感染程度分别与传染媒介的传染概率和传播延迟呈对数关系,无标度网络中流行病的感染程度与传染媒介的传染概率呈幂率关系,而与传播延迟之间则存在线性关系。     

Tracking Consensus for Second-Order Multi-Agent Systems with Nonlinear Dynamics in Noisy Environments

This paper investigates the leader-following tracking consensus problem for second-order multi-agent systems with time delays and nonlinear dynamics in noisy environments on the conditions of fixed and switching directed topologies. Based on a novel velocity decomposition technique and stochastic analysis, a measurement-based distributed tracking control protocol is proposed, under which all agents can track the leader in mean square. Simulation results are also given to illustrate the effectiveness of the proposed protocol.     

Cluster Consensus of Nonlinearly Coupled Multi-Agent Systems in Directed Graphs

We investigate the cluster consensus problem in directed networks of nonlinearly coupled multi-agent systems by using pinning control. Depending on the community structure generated by the group partition of the underlying digraph, various clusters can be made coherently independent by applying feedback injections to a fraction of the agents. Sufficient conditions for cluster consensus are obtained using algebraic graph theory and matrix theory and some simulations results are included to illustrate the method.     

复杂网络中考虑不完全免疫的病毒传播研究

复杂网络中不完全免疫包括免疫失败和免疫失效两种情况,本文研究两者同时存在对网络病毒传播行为的影响,基于平均场理论,提出一种新的传播模型.理论分析表明,免疫失败和免疫失效同时存在显著降低了网络的传播临界值,增强了病毒的感染程度.根据传播临界值与免疫节点密度、免疫成功率以及免疫失效率之间的关系,给出有效控制网络病毒传播的策略.通过数值仿真进行验证。     

Controllability of Discrete-Time Multi-Agent Systems with Multiple Leaders on Fixed Networks

This paper investigates controllability of discrete-time multi-agent systems with multiple leaders on fixed networks. The leaders are particular agents playing a part in external inputs to steer other member agents. The followers can arrive at any predetermined configuration by regulating the behaviors of the leaders. Some sufficient and necessary conditions are proposed for the controllability of discrete-time multi-agent systems with multiple leaders. Moreover, the case with isolated agents is discussed. Numerical examples and simulations are proposed to illustrate the theoretical results we established.     

Simple Majority Consensus in Networks with Unreliable Communication

In this work, we analyze the performance of a simple majority-rule protocol solving a fundamental coordination problem in distributed systems—binary majority consensus—in the presence of probabilistic message loss. Using probabilistic analysis for a large-scale, fully-connected, network of 2n agents, we prove that the Simple Majority Protocol (SMP) reaches consensus in only three communication rounds, with probability approaching 1 as n grows to infinity. Moreover, if the difference between the numbers of agents that hold different opinions grows at a rate of n, then the SMP with only two communication rounds attains consensus on the majority opinion of the network, and if this difference grows faster than n, then the SMP reaches consensus on the majority opinion of the network in a single round, with probability converging to 1 as exponentially fast as n→∞. We also provide some converse results, showing that these requirements are not only sufficient, but also necessary.     

Weighted Evolving Networks with Self-organized Communities

In order to describe the self-organization of communities in the evolution of weighted networks, we propose a new evolving model for weighted community-structured networks with the preferential mechanisms functioned in different levels according to community sizes and node strengths, respectively. Theoretical analyses and numerical simulations show that our model captures power-law distributions of community sizes, node strengths, and link weights, with tunable exponents of v ≥ 1, γ 〉 2, and α 〉 2, respectively, sharing large clustering coefficients and scaling clustering spectra, and covering the range from disassortative networks to assortative networks. Finally, we apply our new model to the scientific co-authorship networks with both their weighted and unweighted datasets to verify its effectiveness.     

Controllability of Discrete-Time Multi-Agent Systems with Multiple Leaders on Fixed Networks

This paper investigates controllability of discrete-time multi-agent systems with multiple leaders on fixed networks. The leaders are particular agents playing a part in external inputs to steer other member agents. The followers can arrive at any predetermined configuration by regulating the behaviors of the leaders. Some sufficient and necessary conditions are proposed for the controllability of discrete-time multi-agent systems with multiple leaders. Moreover, the case with isolated agents is discussed. Numerical examples and simulations are proposed to illustrate the theoretical results we established.     

Robustness measurement of scale-free networks based on motif entropy

As a classical complex network model, scale-free network is widely used and studied. And motifs, as a high-order subgraph structure, frequently appear in scale-free networks, and have a great influence on the structural integrity, functional integrity and dynamics of the networks. In order to overcome the shortcomings in the existing work on the robustness of complex networks, only nodes or edges are considered, while the defects of high-order structure in the network are ignored. From the perspective of network motif, we propose an entropy of node degree distribution based on motif to measure the robustness of scale-free networks under random attacks. The effectiveness and superiority of our method are verified and analyzed in the BA scale-free networks.