Analysis Of Sierpinski Networks And Its Synchronization

Incompatible networks Sierpinski networks, which are induced by the famous Sierpinski fractals, can describe a large class of systems in real life ,for example in the road system of city, interpersonal communication system, biological systems and so on. So it is significant to analyze Sierpinski networks and study on its synchronization.The fundamental works of this paper are summarized as follows:In part one, we will analyze and study Sierpinski networks. Especially, we will analyze and study degree correlations, average path length and clustering coefficient of Sierpinski SG3 (t ) networks by analytical calculation and numerical simulation.In part two, we will study the synchronization of Sierpinski SG3 (t ) dynamic networks. Especially, we will analysis synchronization performance of Sierpinski dynamic networks at first step, which is added chaotic Lorenz system on nodes. Then it is respectively to simulate synchronization of Sierpinski dynamic networks at first step and second step. Finally, it is to analysis its simulation results.In part three, we will improve synchronization performance of Sierpinski dynamic network SG3 (2) by the method of random connection. We present one model with random inserting side into SG3 (2) network and the other model with random reconnecting sides of SG3 (2) network.Then it is to simulate their synchronization. Finally, we obtain that synchronization performance of Sierpinski SG3 (2) dynamic network is really improved.In part four, adding chaotic Lorenz system on nodes, we will simulate synchronization performance of Sierpinski dynamic network.