Existence of periodic solutions for a discrete-time bidirectional neural networks

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 continuous-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 example is also worked out to demonstrate the advantages of our results.