Global attractivity of a synchronized periodic orbit in a delayed network ✩

We consider an artificial neural network where the signal transmission is of a digital (McCulloch– Pitts) nature and is delayed due to the finite switching speed of neurons (amplifiers). For a particular connection topology, we show that all solutions starting from nonoscillatory initial states will be eventually synchronized and stabilized at a unique limit cycle, and hence such a network can be used as a synchronized oscillator.  2003 Elsevier Science (USA). All rights reserved.