Lumping Izhikevich neurons

We present the construction of a planar vector field that yields the firing rate of a bursting Izhikevich neuron can be read out, while leaving the sub-threshold behaviour intact. This planar vector field is used to derive lumped formulations of two complex heterogeneous networks of bursting Izhikevich neurons. In both cases, the lumped model is compared with the spiking network. There is excellent agreement in terms of duration and number of action potentials within the bursts, but there is a slight mismatch of the burst frequency. The lumped model accurately accounts for both intrinsic bursting and post inhibitory rebound potentials in the neuron model, features which are absent in prevalent neural mass models.