Synchronization Of Two Kinds Of Fractional-order Complex-valued Neural Networks With Delay

Artificial neural network has attracted much attention because of its great application prospects,such as pattern recognition,solving nonlinear equations,secure communication and so on.Fractional-order calculus has infinite memory and hereditary nature.So the combination of fractional-order calculus and neural network can more accurately describe the dynamic characteristics of neural network.In recent years,the research on the dynamic behavior of fractional-order neural network,such as bifurcation,stability and synchronization,has become a hot spot.The classical method of neural network research is decomposition method that the system is divided into two real valued systems.Based on the existing research,this paper studies the complex value system as a whole by direct method.Two problems are discussed in this paper.The first one is to study the finite-time synchronization of fractional-order complex-valued neural networks with time delay.Firstly,a series of differential inequalities are introduced,and two control schemes based on quadratic norm and absolute norm are given.Then by constructing a suitable Lyapunov function,using the theory of complex variable function and inequality technique,the criteria of finite-time synchronization and the stable time are obtained.The second one is to discuss the complete synchronization of fractional-order complex-valued neural networks with delay and unknown parameters.The coefficients of fractional-order complex-valued neural networks are set as unknown parameters related to time.And the conditions of full synchronization are obtained by constructing Lyapunov function under the adaptive controller.Finally,we summarize the main points and innovations of this paper.Looking forward to the future,we reflect on the shortcomings of this paper and determine the next research direction.