Intrinsic modulation of pulse-coupled integrate-and-fire neurons

Intrinsic neuromodulation is observed in sensory and neuromuscular circuits and in biological central pattern generators. We model a simple neuronal circuit with a system of two pulse-coupled integrate-and-fire neurons and explore the parameter regimes for periodic firing behaviour. The inclusion of biologically realistic features shows that the speed and onset of neuronal response plays a crucial role in determining the firing phase for periodic rhythms. We explore the neurophysiological function of distributed delays arising from both the synaptic transmission process and dendritic structure as well as discrete delays associated with axonal communication delays. Bifurcation and stability diagrams are constructed with a mixture of simple analysis, numerical continuation and the Kuramoto phase-reduction technique. Moreover, we show how realistic forms of voltage dependent shunting synaptic currents can act to limit the firing rate of the system, and that, for asynchronous behaviour, the strength of electrical synapses can control such rates. 87.10+e, 0.2.30.Ks, 47.20.Ky