Studying On Synchronization Of Small World Complex Network Based On Dual-ring Erbium-doped Fiber Laser

In nature and human society, the complex network can be seen everywhere, such as the Internet, power grids, neural network and social networks, etc, and they all can be regarded as a complex network. Therefore, the study of modeling and characteristic of complex network has very important academic significance and practical application value. Based on hyper-chaotic system of the dual-ring erbium-doped fiber laser, in this letter, to study the characteristics of synchronization in one network and two networks, different complex network model are constructed. This paper introduces the main work as follows:(1) Firstly, analysis the hyper-chaos behaviors of dual-ring erbium-doped fiber laser, as well as hyper-chaotic synchronizations characteristics of two dual-ring erbium-doped fiber laser are studied. Based on Lyapunov function theorem, a reasonable controller and parameters of the response system are design. Simulation results show that synchronization between the driver-response system of dual-ring erbium-doped fiber laser is well completed.(2) Second, constructs a ten node small world random networks with dual-ring erbium-doped fiber laser hyper-chaos system, and realize the internal synchronization of it. On this basis, construct ten nodes NW and eight nodes WS small-world network respectively. The controller and the parameters in response system are improved by method of Lyapunov function. Simulation results show that the internal synchronization and external synchronization in small world complex network are obtained perfectly.(3) Finally, still using hyper-chaos of dual-ring erbium-doped fiber laser as network nodes to study the synchronization between scale-free network and small world network. Constructs a scale-free network of ten nodes, and design the controller by Lyapunov function method. Then synchronization between ten nodes scale-free network and eight nodes WS small world network is completed effectively. Simulation results show that two network reached the synchronization successfully.At present, the optical chaotic systems, especially the complex network composed of optical hyper-chaotic systems have important research value due to their unique properties. However, the research, development and application in this field has not been very mature yet. Therefore, in this paper, based on dual-ring erbium-doped fiber laser, the research of synchronization characteristics of hyper-chaotic system in complex random networks has good reference value.