Stability Analysis Of Fractional-Order Neural Network With Time-Delay

Fractional order neural network is an extension and deepening of the integer order neural network.It is more important for the complexity of the dynamical system and the accuracy of the description of the neuron.In this paper,based on fractional order Lyapunov stability theory,functional analysis method,matrix inequality technique and contraction fixed point theorem,we study the issue of the Mittag-Leffler stability,asymptotic stability and global O(t^-p)stability.The main contents are as follows:Firstly,the Mittag-Leffler stability of a class of recursive fractional neural networks with constant delay is studied.With the construction of Lyapunov function and the technique of some delay differential inequalities,the boundedness of the system and the sufficient condi-tions of the system Mittag-Leffler are obtained.Three sets of numerical values are selected to simulate the experiment and verify the validity of the results.Then,through the fractional Lyapunov stability theorem,extended on the previous ba-sis,the asymptotic stability of fractional neural networks with time-varying delay is studied.Using the contraction fixed point theorem prove existence and uniqueness of the equilibrium point,by using the functional method obtained the sufficient conditions for the asymptotic stability of the system,and take more groups of initial value of the two numerical examples verify the validity of the results.Finally,the fractional neural network of neural excitation function with proportional delay is studied,by constructing suitable Lyapunov function and appropriate assumption-s obtained the sufficient conditions for the global O(t^-p) stability of the system,and two numerical examples are simulated to further verify the accuracy of the results.