  We study the time delay in the synaptic conductance for suppression of spike
synchronisation in a random network of Hodgkin Huxley neurons coupled by means
of chemical synapses. In the first part, we examine in detail how the time
delay acts over the network during the synchronised and desynchronised neuronal
activities. We observe a relation between the neuronal dynamics and the syaptic
conductance distributions. We find parameter values in which the time delay has
high effectiveness in promoting the suppression of spike synchronisation. In
the second part, we analyse how the delayed neuronal networks react when pulsed
inputs with different profiles (periodic, random, and mixed) are applied on the
neurons. We show the main parameters responsible for inducing or not
synchronous neuronal oscillations in delayed networks.
