Delay induced periodicity in a neural netlet of excitation and inhibition

Abstract

The dynamical behaviour of a two neuron netlet of excitation and inhibition with a transmission delay is investigated. It is shown that in the absence of delay, the netlet relaxes to the trivial resting state. If the delay is of sufficient magnitude, the network is excited to a temporally periodic cyclic behaviour. The analytical mechanism for the onset of cyclic behaviour is through a Hopf-type bifurcation. Approximate solusions to the periodic output of the netlet is calculated; stability of the temporally periodic cycle is investigated. It is shown that the bifurcation is supercritical. A related discrete version of the continuous time system is formulated. It is found that the discrete system also displays a cyclic behaviour. Results of a number of computer simulations are displayed graphically; the article concludes with a brief neurobiological discussion.