Periodic Solutions to a Modified Elman Neural Network

Elman neural network is a recurrent neural network. Compared with traditional neural networks, an Elman neural network has additional inputs from the hidden layer, which form a new layer called the context layer. The standard back-propagation algorithm used in Elman neural networks is called back-propagation algorithm. Elman neural networks can be applied to solve prediction problems of discrete-time sequences. In the present paper, for a modified Elman neural network with a periodic input, we present sufficient conditions for the existence of a periodic output by using Mawhin's continuation theorem of the coincidence degree theory. Examples are given of Elman neural networks satisfying these sufficient conditions. Periodic solutions are found for particular choices of the weights, self-feedback factor and periodic inputs. Further on, sufficient conditions are presented for the global asymptotic stability of a periodic output. The periodic outputs corresponding to the solutions previously found are shown to be globally asymptotically stable for any continuous transfer functions of the output layer.