Robustness And Calculations Of Coherence On Many Kinds Of Recursive Networks

Complex networks have been proved as an important tool to describe complex systems in real world.Studying the relationship between network topology and dynamics has always been a hot topic in complex networks.Nowadays,consensus in multi-agent systems with an additive noise has attracted more and more attention with an focus on the impact of network topology on the coherence.As a family of deterministic networks,recursive networks have the advantage that they can analytically analyze and calculate the topological properties and dynamics of the network,e.g.,synchronizability and network coherence.In this dissertation,many kinds of recursive networks are chosen as the network models.Using the regular network topology and matrix operations,the analytical results of Laplacian spectrum and exact expressions of network coherence are obtained.Further,the influence of network parameters and number of leaders on network coherence is investigated.In details,the main works are as follows:The first chapter introduces the research background and current progress of complex networks,and describes the definition of consensus problem with the noise.The second chapter studies network coherence in a family of book graphs.Using the topological structures of book graphs,we obtain recursive relationships for the Laplacian matrix and Laplacian eigenvalues and further derive exact expressions of the network coherence.Finally,we illustrate the robustness of network coherence under the graph parameters and show that the parameters have distinct effects on the coherence.The third chapter solves the leader-follower coherence with many preassigned leaders.The leaderless coherence and the leader-follower coherence quantified by the Laplacian spectrum,are applied to noisy windmill graphs.Based on the graph construction,exact solutions are obtained for the leader-follower coherence with freely assigned leaders.In order to compare consensus dynamics of two non-isomorphic graphs with the same number of nodes and edges,two generalized windmill graphs are selected as the network models and then explicit expressions of the network coherence are obtained.Finally,the robustness of the coherence is analyzed.Accordingly,it is found that graph parameters and the number of leaders have a profound impact on the studied consensus algorithms.The fourth chapter is a summary of this dissertation and future works.