Periodic solutions for a delayed neural network model on a special time scale

This paper concerns a delayed neural network model x Δ ( t ) = − 1 2 x ( t ) + f ( x ( t − 2 ) ) , t ∈ T = ⋃ k = 0 ∞ [ 2 k , 2 k + 1 ] . Here T is a special time scale, and f is a signal transmission function. According to the discontinuity of signal function, by iteration, we obtain the existence of periodic solutions of the model and their asymptotical stability.