Cortical activity exhibits complex, persistent self-sustained dynamics, which is hypothesised to support the brain’s sophisticated processing capabilities. Prior studies have shown how complex activity can be sustained for some time in spiking neural network models, but network activity in these models resembled high firing rate seizure which would eventually fail, leading to indefinite quiescence. We present a spiking network model of cortex innervated by diffuse thalamic projections, called the Complex Spiking Model (CSM). The model exhibits persistent, self-sustained, non-periodic, complex dynamics at low firing rates. Multiple network configurations were tested, systematically varying diffuse excitation from the thalamus, strength of the local cortical inhibition and excitation, neighbourhood diameters, synaptic efficacies and synaptic current time constants. Complex activity in all the network configurations depended strongly upon the strength of the diffuse excitation from the ...