Research On Synchronization Control Of Fractional-order Complex System And Its Application In Image Encryption

Complex networks is a new subject,which has been studied extensively by scholars in various fields.At present,the research on complex networks mainly focuses on its synchronization control.In order to increase the order variability of complex network systems,fractional-order systems have great potential in characterizing the process of state change of materials with memory and genetic properties,the Fractional Calculus is introduced into the complex network system to establish the fractional-order complex network system.Fractionalorder complex networks have more complex dynamic characteristics,so they have more extensive application prospects.In addition,communication delay exists widely in nature and engineering systems,which has an important influence on the research of network synchronization.Based on the above considerations,the main research contents of this paper can be summarized as follows:Firstly,for the synchronization problem of coupled fractional-order complex networks with arbitrary fixed topology,a scheme for selecting tie nodes is presented.Based on the Lyapunov stability theory,a sufficient condition for the synchronization of a coupled fractional order complex network is derived by designing a suitable controller.Moreover,the results are generalized to the system of integer-order.Finally,the above theoretical results are verified by simulation.Secondly,the synchronization problem of coupled fractional-order neural networks with time-delay is studied considering the influence of external factors on communication delay.By introducing a control scheme and using the techniques of Matrix inequality and Young inequality,the synchronization of a coupled fractional-order neural network with time delay is accomplished.Thirdly,the types of communication delay are analyzed,and the problem of projective synchronization for fractional-order neural networks with distributed and discrete delays is studied.An improved Halanay inequality is proposed as a theoretical analysis tool.Based on the Lyapunov stability theory,by constructing appropriate Lyapunov functions,the necessary conditions for the network to achieve synchronization are obtained.The numerical simulation verifies the correctness of the theoretical results.Finally,the synchronization of the fractional-order complex network is applied in the image encryption field,and good results are obtained.