Adaptive synchronization on complex dynamical networks

Today, complex networks have attracted increasing attention from various fields of science and engineering. It has been demonstrated that many complex networks display various synchronization phenomena. This letter studies adaptive synchronization in regularly coupled complex dynamical networks. An adaptive coupling strength algorithm is proposed to effectively stabilize and synchronize complex networks. The strictness proof of this algorithm from the viewpoint of mathematics is given. Especially, we show that synchronization of such complex dynamical networks is completely determined by the coupling strength. An examples is simulated, using the chaotic Lorenz system, as the nodes of the complex dynamical networks, which demonstrate the effectiveness of the proposed adaptive algorithm.