The Consistency Of Multi-agent Network, And Synchronization Of Chaotic Systems

Complex networks have been considered as an important approach for describing and understanding complex systems by many researchers recently. From the movement of molecules within our cells to communication across an entire planet, we are part of networks. This special section shows how scientists are pushing network analysis to its limits across disciplinary fields. Today the understanding of networks is a common goal of an unprecedented array of traditional disciplines:Cell biologists use networks to make sense of signal transduction cascades and metabolism; computer scientists are mapping the Internet and the WWW; epidemiologists follow transmission networks through which viruses spread; and brain researchers are after the connectome, a neural-level connectivity map of the brain.Noise is commonly regarded as a random and persistent disturbance obscuring or reducing the clarity of a signal. The role of noise in network systems is quite versatile. In certain cases noise is detrimental to the stability of the networks. In certain cases it's presences is necessary, noise can be used to stabilize a given unstable system or to make a system even more stable when it is already stable. Since noise is ubiquitous in both nature and manmade systems, it is necessary to consider the effect of noise on the dynamics of network systems.Recently, consensus problems of multi-agent networks have attracted a great deal of attention in many fields. This is partly due to broad applications of multi-agent sys-tems in many areas including cooperative control of unmanned air vehicles, formation control, attitude alignment of clusters of satellites, and congestion control in communi-cation networks. Based on the work of many researchers, this dissertation extend the previous results of consensus in networks of multi-agents. The effect of noise, commu-nication time-delay and the switching topology are considered.Chaos synchronization is of fundamental importance in secure communication, and nano-oscillators, etc. Since noise is ubiquitous in both nature and manmade sys-tems, synchronization of concrete models is unavoidably subject to internal and exter-nal noise. Recently, synchronization in noise-perturbed chaotic systems was studied by many researchers. In this dissertation, the synchronization of the noise-perturbed time-delayed systems and two different systems are investigated.In addition, the synchronization of hand clapping, and the stability, bifurcation and chaos of the epidemic model on small-world networks are also considered. These results are significant not only in mathematical theory but also in many applied fields. The main work in this dissertation is listed as follows:In chapter 1, the research background and progress on complex networks and chaos synchronization are introduced. Moreover, some preliminaries and the structure of this dissertation are given.In chapter 2, the consensus problems on networks of multi-agent systems in noisy environment are presented. Firstly the average consensus problem is considered. Then the average consensus problem with time delay and the leader-following consensus problem with time delay are considered. Finally the average consensus problem with noise coupling is investigated. Based on the stability theory of stochastic differential equations, the sufficient conditions ensuring the successful consensus are given. Both the theoretical and numerical results show that the speed of convergence in the environ-ments with large noise intensity is lower than that in the environments with relatively small noise intensity, the strong noise even can prevent the consensus from occurring.In chapter 3, synchronization of the applause with leaders is investigated. Two cases of the effect of the applause transmission time delays on the spectators are con-sidered. Sufficient conditions for the applause synchronization are presented for both cases. The established theoretical results not only support the observation that it is easy to hear the rhythmic applause in a theater with high attendance rate, but also show a sur-prising conclusion that one leader is enough to make all spectators clap with the same frequency in a very large theater.In chapter 4, a nonlinear epidemic model in small-world networks with time-delay is presented to investigate the impact of the treatment measures on the epidemic dynam-ics. Local stability and Hopf bifurcation are considered. It is shown that the strength of treatment measures not only determine the stability of the local equilibrium, but also can be applied to stabilize a periodic or chaotic spreading behavior onto a stable equi-librium.In chapter 5, the synchronization of noise-perturbed chaos systems is investigated. Firstly complete synchronization and anti-synchronization of a class of coupled time-delayed systems with parameter mismatch and noise perturbation are investigated. Suf-ficient conditions guaranteeing complete synchronization and anti-synchronization with constant and varying time delay are developed. Then chaos synchronization between Lorenz system and one of the noise-perturbed Chen and Lu systems is investigated. Based on the Lyapunov theory in stochastic differential equations, sufficient conditions for the stability of the error dynamics are derived.At the end of this dissertation, the conclusions and some topics for future work are given.