Research On Various Synchronizations Of Fractional-order Neural Networks And Its Application

Neural network is a mathematical model that simulates the structure and function of the human brain.Due to its advantages of distributed storage,fault tolerance and parallel processing,the theoretical and applied research on the dynamical behavior of neural network has received increasingly widespread attention.Synchronization is a major dynamical behavior of neural networks.It is widely used in various fields,respectively in physics,mathematics,computer science,biological sciences and social sciences.The fractional-order neural network,which combines fractional-order calculus and neural network,is a beneficial improvement to traditional integer-order neural network.Therefore,studying the dynamical behavior of fractional-order neural network can enrich the stability theory of neural network and promote their applications in areas such as image processing,secure communication and associative memory.This paper investigates multiple synchronization control of fractionalorder neural network.The research content consists of the following parts:The first part investigates the output synchronization of coupled fractional-order neural networks.Based on Lyapunov’s stability theorem and the properties of fractional-order algorithms,sufficient conditions are derived to guarantee the output synchronization of coupled fractional-order neural networks with fixed coupling.Moreover,the adaptive strategy with adjustable coupling weights is introduced,and sufficient conditions are proposed for guaranteeing the output synchronization of fractional-order neural networks with adaptive couplings.Compared with previous results,the results of this paper are not only applicable to fractional-order systems but also to integer-order systems.Finally,the validity of the results is verified by numerical simulations.The second part investigates the bipartite synchronization for coupled multi-order fractional-order neural networks with time-varying delays.An efficient event-triggered controller is proposed,and the sufficient criteria for ensuring bipartite synchronization is derived by using the comparison principle of multi-order fractional-order differential equations and Lyapunov functions in vector form.In addition,it discusses whether Zeno behavior can occur under event-trigger control.The results obtained in this paper cover the bipartite synchronization of both fractional-order neural networks with identical order and integer-order neural networks as special cases,the validity of the theoretical results is verified by numerical simulations.The third part investigates the finite-time synchronization of fractional-order driven response neural networks with time-varying delays.Based on the properties of fractionalorder differentiation and the Lyapunov direct method,sufficient criteria for achieving finitetime synchronization in fractional-order driven response neural networks are given.The results are also applied to fractional-order driven response neural networks without timevarying delays and integer-order systems,and the validity of the results is verified by two simulation examples.The fourth part proposes an image encryption method based on finite-time synchronization of fractional-order driven response system.The chaotic signal is obtained by fractional-order driven response system and combined with binary Xor operation,equal area mapping scrambling and other methods to encrypt the image.Then the response system used to obtain the decryption matrix and the inverse operation of the encryption method used to decrypt the encrypted image.The feasibility of the method is also analyzed.