Study On Function Projective Synchronization Of Complex Networks With Unknown Topological Structure And Parameters

The synchronization of complex networks is not only closely related to our daily life but also closely related to the research fields of physics,mathematics,biology and computer science.Research of complex network synchronization has an important scientific significance and a wide range of potential applications.This thesis mainly studies the function projective synchronization of complex network with unknown topological structure and parameters.Compared with the general network projection synchronization,it has better security and anti jamming ability in the practical application of information communication and other fields.The specific research contents of this paper are as follows:First of all,it introduces the complex network development process,the basic concepts of complex networks,typical complex network model and network basic properties.At the same time,researches of the complex networks are analyzed and its practical applications are also introduced.Secondly,it summarizes the type of synchronization on the network,introduces several common methods of network synchronization and synchronization control of the corresponding principle.On this basis,the projective synchronization of complex networks with uncertain topological structure and parameters is achieved by the adaptive method.The error variables of complex network dynamics equation are defined,base on the Lyapunov stability theorem and the adaptive control method,the network achieves synchronization conditions.The network model with unknown topological structure is constructed by the optical bistable chaotic system,and the feasibility of the theoretical analysis is verified by numerical simulation.In the process of the synchronization of the network nodes,the uncertain topological structure and parameters are also obtained.Further,the projective synchronization theory is extended to the investigation of the function projective synchronization of the network.The Lyapnunov function is constructed by using the error equation.Later on the unknown parameters can be identified.The identification rate and the change rate of the function scale factor are obtained.Taking stimulated Raman scattering chaotic system as nodes to construct the network dynamics equation,the simulation results show that the synchronization of network is extremely stable.