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.