Stable periodic orbits in nonlinear discrete-time neural networks with delayed feedback (Q1827153)

The authors consider a nonlinear discrete-time system \(x(n+1) = x(n)+g(y(n-k))\), \(y(n+1) = y(n)-g(x(n-k))\), \(n\in \mathbb{N}\) arising as a discrete-time network of two neurons with McCulloch-Pitts nonlinearity, where \(\beta\in (0,1), k\) is a positive integer, and \(g\) is a signal transmission function with a threshold \(\sigma\). The authors show that there exist a stable \(4(k+1)\)-periodic orbit in some regions of the parameters \((\beta,\sigma)\), and analyses asymptotic behavior of the system in other regions of \((\beta,\sigma).\)