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), 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.