S-asymptotically ?-periodic Solution And Hyers-Ulam Stability For Fractional-Order Neural Networks

Fractional calculus is the generalization of integer-order calculus.It is found that fractional-order differential equations can describe the memory and"heredity" more fully than integer-order differential equations.Scientific and engineering problems can be better solved by fractional-order differential equations.The object of this study is the fractional-order neural network model,which is actually a system,so we are indispensable to study its periodicity and stability.Many scholars have demonstrated in detail that there is no periodic solution for the non-autonomous neural network based on the Caputo derivative.When combined with the fact that the parameters in the actual system are affected by various factors,the change of parameters can be seemed as approximately periodic.Therefore,the asymptotical periodic.ity,the asymptotical w-periodicity and the s-asymptotical w-periodicity are posed and studied gradually.On this basis,we will further study the existence of the s-asymptotically w-periodic solution of the fractional-order neural network.Stability is one of the important preconditions to ensure the normal operation of the system.To discuss the stability of the fractional-order neural network can ensure the rationality of the system.At present,there are many studies on the Mittag-Leffler stability of the fractional-order neural network.In this thesis,some work has been done for the less studied Hyers-Ulam stability.The difference between Hyers-Ulam stability and Mittag-Leffler stability is that Hyers-Ulam stability can reflect the influence of small error disturbance on the system.The main contents of this thesis are as follows.Firstly,the fractional-order neural network with constant coefficients is studied:(?) Different from the traditional method of using Volterra integral to express the solution of fractional-order neural network,this thesis mainly uses Mittag-Leffner functions to ex-press the solution of fractional-order neural network.Making full use of the properties of Mittag-Leffler functions and by the contraction mapping principle,we get the existence and uniqueness of its s-asymptotically w-periodic solution.An example is given to verify the validity of the result.Secondly,the Hyers-Ulam stabilities of two types of fractional-order neural network models are studied.One is the fractional-order neural network with constant coefficients:(?) The existence and uniqueness of its solution on J and the stability of Hyers-Ulam are proved and given a numerical example to verify the validity of the theorem.The other is the fractional-order neural network model with variable coeffocients:(?)The existence and uniqueness of its solution on J and the stability of Hyers-Ulam are also proved and given a numerical example to verify the validity of the theorem.