Neural Comput - On the continuous differentiability of inter-spike intervals of synaptically connected cortical spiking neurons in a neuronal network.

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Resumo

We derive conditions for continuous differentiability of inter-spike intervals (ISIs) of spiking neurons with respect to parameters (decision variables) of an external stimulating input current that drives a recurrent network of synaptically connected neurons. The dynamical behavior of individual neurons is represented by a class of discontinuous single-neuron models. We report here that ISIs of neurons in the network are continuously differentiable with respect to decision variables if (1) a continuously differentiable trajectory of the membrane potential exists between consecutive action potentials with respect to time and decision variables and (2) the partial derivative of the membrane potential of spiking neurons with respect to time is not equal to the partial derivative of their firing threshold with respect to time at the time of action potentials. Our theoretical results are supported by showing fulfillment of these conditions for a class of known bidimensional spiking neuron models.

Resumo Limpo

deriv condit continu differenti interspik interv isi spike neuron respect paramet decis variabl extern stimul input current drive recurr network synapt connect neuron dynam behavior individu neuron repres class discontinu singleneuron model report isi neuron network continu differenti respect decis variabl continu differenti trajectori membran potenti exist consecut action potenti respect time decis variabl partial deriv membran potenti spike neuron respect time equal partial deriv fire threshold respect time time action potenti theoret result support show fulfil condit class known bidimension spike neuron model

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