STABILITY OF PERIODIC OSCILLATIONS IN A NETWORK OF NEURONS WITH TIME-DELAY

Oscillatory behavior is investigated in the case of a network of oscillatory pairs of neurons with time-delayed connections. The uniform periodic solution is obtained from the numerical integration of a system reduced to a single pair of neurons. The stability of this periodic orbit in the network is estimated from a discretization of the time axis. It is shown that the periodic solution becomes unstable as the size of the system is increased. This loss of stability results in the appearance of spatiotemporally structured behavior, such as travelling waves.