DELAY INDUCED PERIODICITY IN A NEURAL NETLET OF EXCITATION AND INHIBITION

The dynamical behaviour of a two neuron netlet of excitation and inhib ition with a transmission delay is investigated. It is shown that in t he absence of delay, the netlet relaxes to the trivial resting state. If the delay is of sufficient magnitude, the network is excited to a t emporally periodic cyclic behaviour. The analytical mechanism for the onset of cyclic behaviour is through a Hopf-type bifurcation. Approxim ate solutions to the periodic output of the netlet is calculated; stab ility of the temporally periodic cycle is investigated. It is shown th at the bifurcation is supercritical. A related discrete version of the continuous time system is formulated. It is found that the discrete s ystem also displays a cyclic behaviour. Results of a number of compute r simulations are displayed graphically; the article concludes with a brief neurobiological discussion.