Map-based models in neuronal dynamics

Ever since the pioneering work of Hodgkin and Huxley, biological neuron models have consisted of ODEs representing the evolution of the transmembrane voltage and the dynamics of ionic conductances. It is only recently that discrete dynamical systems–also known as maps–have begun to receive attention as valid phenomenological neuron models. The present review tries to provide a coherent perspective of map-based biological neuron models, describing their dynamical properties; stressing the similarities and differences, both among them and in relation to continuous-time models; exploring their behavior in networks; and examining their wide-ranging possibilities of application in computational neuroscience.