The elapsed-time model describes the behavior of interconnected neurons
through the time since their last spike. It is an age-structured non-linear
equation in which age corresponds to the elapsed time since the last discharge,
and models many interesting dynamics depending on the type of interactions
between neurons. We investigate the linearized stability of this equation by
considering a discrete delay, which accounts for the possibility of a synaptic
delay due to the time needed to transmit a nerve impulse from one neuron to the
rest of the ensemble. We state a stability criterion that allows to determine
if a steady state is linearly stable or unstable depending on the delay and the
interaction between neurons. Our approach relies on the study of the asymptotic
behavior of related Volterra-type integral equations in terms of theirs Laplace
transforms. The analysis is complemented with numerical simulations
illustrating the change of stability of a steady state in terms of the delay
and the intensity of interconnections.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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