Symmetric Bifurcations of FDEs: Theory and Applications to Neural Networks with Memory
Jun Yu Wu · 2020
It has been pointed out by Hopheld(1982, 1984) and Marcus and Westervelt(1989) that in the hardware implementation of neuron networks, neurons(amplihers) do not communicate and respond instantaneously. Experiments and numerical simulations carried out by Marcus and Westervelt(1989) clearly indicated that sustained oscillations can arise from large relative size of the delay(relative to the relaxation time of the system) in the communication and response among neurons. Theoretical study by Belair(1993) , Herz(1993a , b ), Marcus and Westervelt(1989) , and Wu(1993) has further confirmed the existence of sustained oscillaltions induced by large delay, and some stability analysis of these oscillations has been reported in Belair(1993) , Herz(1993a , b ) and Wu and Zou(1994) .