Theoretical foundations of pulse-coupled models

Many scientists believe that all pulse-coupled neural networks are toy models that are far away from the biological reality. We show here that many biologically plausible Hodgkin-Huxley type neural networks can be transformed into a pulse-coupled form by a suitable change of variables. Such transformations exist when a network satisfies a number of conditions-it is weakly connected, the neurons are Class 1 excitable (i.e., they can generate action potentials with an arbitrary small frequency), and the synapses between neurons are conventional (i.e. axo-dendritic and axe-somatic). Thus, the difference between studying the pulse-coupled model and Hodgkin-Huxley type neural networks is just a matter of a coordinate change