Retracted: Existence of Periodic Solutions for a Discrete-Time Bidirectional Neural NetWorks

Abstract

In the present paper, we investigate periodic solutions for a class of discrete-time bidirectional neural networks by a system of non-autonomous difference equations with time delays. The class of systems considered retains the basic structure of the continuous-time bidirectional neural networks with the nonlinearities having infinite gain and inherits the dynamical characteristics of the con-tinuous-time networks under mild or no restriction on the discretization step-size. The theory of coincidence degree and inequality technique instead of the bifurcation method, are employed to prove the existence of periodic solutions for the discrete-time bidirectional neural networks. Without assuming the smoothness and boundedness of the activation functions, the easily checked conditions ensuring the existence of periodic solutions for the discrete-time bidirectional neural networks are obtained. The results of this paper extend and improve partly the previous ones and can be used in other autonomous neural networks. An ex-ample is also worked out to demonstrate the advantages of our results.