Synchronization and synchronized periodic solution in a simplified five-neuron BAM neural network with delays

A delay-differential equation, modeling a bidirectional associative memory (BAM) neural network with five neurons, is considered. Some results of synchronization and bifurcation are exhibited. By Lyapunov functional methods, some sufficient conditions for the absolute synchronization of the system and global attractivity of the trivial solution are established. This synchronization is independent of the size of time delay. Furthermore, delay-induced synchronized periodic solution is given analytically, as well as necessary and sufficient conditions for the synchronized periodic solution by perturbation-incremental scheme (PIS). The main difference in this paper from previous works in the literatures is that delay-induced synchronization is studied quantitatively. Theoretical results are illustrated with numerical simulations.