Adaptive In The Synchronization Research Applications Of Complex Network

Nowadays, humanity has come to network age. Network of human society requires us to have a better understanding of the behaviors and characteristics of complex dynamical network which is natural or artificial. Studying the quantitative and qualitative characteristics of complex network has become an important challenging research topic in the network times. Currently, researching of complex network focuses on synchronization, consistency, stabilization. Especially, synchronization, one of the typical collective behaviors of complex dynamical networks, has been investigated for many years and numerous significant works have been done.The synchronization of complex network is investigated by using adaptive idea in this thesis. Adaptive idea is an effective tool to solve the uncertainty and some complex factors of complex network because of the self-adjusting and robustness. In addition, some other good control strategies are also adopted to combined with adaptive idea which can take advantage of the advantages of adaptive.In this thesis, three different control strategies are applied to investigate the synchronization of three types complex network, respectively. It contains 1) A array of adaptive controller are designed to realize the synchronization of an uncertain complex network with two types of time-varying delays. 2) Based on Barbalat's lemma, two adaptive pinning control strategies are derived to study the projective synchronization of the drive-response dynamical network of partially linear systems. 3) For a complex dynamical network with constant delays, the stability results for the impulsive dynamical system is utilized. A globally synchronization criteria is proposed and a hybrid controller, which contains an adaptive controller and an impulsive controller, is designed. From simulation, the control effect of hybrid control is better than the single control scheme. For the three investigation results, the corresponding numerical simulations are presented to demonstrate the effectiveness of those results.