Stable periodic orbits in nonlinear discrete-time neural networks with delayed feedback

We consider a nonlinear discrete-time system x(n+1) = βx(n)+g(y(n-k)), y(n+1) = βy(n)-g(x(n-k)), n εN arising as a discrete-time network of two neurons with McCulloch-Pitts nonlinearity, where β ε (0,1), k is a positive integer, and g is a signal transmission function with a threshold σ. We obtain a stable 4(k+1)-periodic orbit in some regions of the parameters (β,σ) and we describe asymptotic behaviors of the system in other regions of (β,σ).