Influence Of Network Topologies And Edge Weights On Group Consensus

As the basis of the cooperative and coordinated control of agents,the consensus behavior is a significant theoretical problem in complex dynamical systems.Group consensus means that states of agents reach at the same value through agents' local coupled interactions in the system.As a burgeoning interdiscipline,network science provides a lot of practical methods,models and tools.For a systematic understanding and analysis of the dynamical processes on the network,it is needed that the network properties are incorporated in the research.The topological nature of a network depends only on the number of nodes and on which edges are connected in the network.Considering that different edges may have different link strength,real-world networks are usually weighted,and the nature of edge weights will also influence the evolution of dynamical processes.This dissertation focuses on the influence of the variation of network topologies and edge weights on group consensus.Firstly,the influence of network topologies' changes induced by leader selection on the convergence speed of consensus algorithms is analysed.Then,the influence of network edge weights' changes generated by quantization on the convergence speed is studied.Finally,the effects of the weighted networks which are generated from the DeGroot-Friedkin(DF)model on the level and convergence speed of group consensus are investigated.The main contributions of this dissertation are summarized as follows:1.Investigation on the influence of leader selection in networks on group consensus.Consider a leader-follower multi-agent model,the consensus centrality(CC)of a node is defined as the minimum eigenvalue of the principle diagonal submatrix of Laplacian,which quantifies how fast a leader could guide the corresponding followers' network to achieve the desired consensus.Because different nodes denote different convergence speeds,the goal of this chapter is to design some simple and easy strategies to fast find the node with the maximum CC.Simulations in real-world networks,randomly rewired networks and synthetic networks show the long-tailed distribution of the proposed centrality,and its correlation with other node centralities,and the effects of a network's heterogeneity and density on CC.Because of the highly positive correlation between CC and degree in all the networks,a leader selection strategy based on degree is proposed.Finally,considering the topological nature of the centrality in networks,a heuristic single leader selection algorithm is proposed which can be applied in large-scale networks.Simulations in real-world networks demonstrate that the algorithm can find at least a suboptimal leader fast and effectively.2.Investigation on the influence of edge weights' quantization in networks on group consensus.Many networks we constructed and investigated in network science studies are based on quantized weights of edges for convenience or due to limitation on measurement.An uniform step-like quantization procedure on edge weights is proposed,and its effects on network behaviors such as consensus and synchronizability are investigated based on the spectrum of the corresponding Laplacian.A zigzaged decline and periodic jumping phenomenon of the eigenvalues are observed as the quantization level increases,which demonstrates that there exists a critical quantization level that makes a better approximation of the quantized network to the original one.Moreover,the peak-value decreasing in a power-law relationship is found.Explanations and analyses are given based on the eigenvalue perturbation theory and the heterogeneity of edge weight distribution.Besides,the critical role that heterogeneity of edge weight distribution plays in the jumping phenomena is validated through simulations.The factors which affect the critical quantization level are analysed.Futhermore,the method of rounding-off and integralization is applied to non-integer weights in networks.The decreasing behavior of eigenvalues in the corresponding integer networks is found to be the same as that in the original one,and so is the critical quantization level.3.Investigation on the influence of the weighted networks generated based on the DF model on group consensus.Consider a group of individuals with levels of stubbornness who discuss a sequence of repeated similar issues successively under the given relative interaction edge topology,if the edge weights vary according to the reflected appraisal mechanism in the DF model,the evolution of the group's certainty of beliefs in the generated steady-state weighted networks is studied.In comparison with the original networks,it is found that in weighted networks group's beliefs' convergence speed is faster,the differences among beliefs are smaller,and the quasi-consensus is reached.Furthermore,the influence of different underlying network models and parameters on the evolution of social power which is also nodes' self-weights,as well as on the belief system dynamics which take place on corresponding weighted influence networks are uncovered.Especially,results display that the most heterogeneous star network leads to the appearance of autocrats such that group's beliefs will reach a consensus on autocrat's belief,but a symmetric nearest neighbor coupled network that is dense enough can ensure the equality of group's influence power,and the average quasi-consensus of group's beliefs as well.