A brief history of excitable map-based neurons and neural networks

This review gives a short historical account of the excitable maps approach for modeling neurons and neuronal networks. Some early models, due to [Pasemann, 1993] and [Chialvo, 1995] and Kinouchi and Tragtenberg (1996), are compared with more recent proposals by Rulkov (2002) and Izhikevich (2003). We also review map-based schemes for electrical and chemical synapses and some recent findings as critical avalanches in map-based neural networks. We conclude with suggestions for further work in this area like more efficient maps, compartmental modeling and close dynamical comparison with conductance-based models.