Complex Dynamic Thresholds and Generation of the Action Potentials in the Neural-Activity Model

Abstract

This work is devoted to studying the processes of activation of the neurons whose excitation thresholds are not constant and vary in time (the so-called dynamic thresholds). The neuron dynamics is described by the FitzHugh–Nagumo model with nonlinear behavior of the recovery variable. The neuron response to the external pulsed activating action in the presence of a slowly varying synaptic current is studied within the framework of this model. The structure of the dynamic threshold is studied and its properties depending on the external-action parameters are established. It is found that the formation of the “folds” in the separatrix threshold manifold in the model phase space is a typical feature of the complex dynamic threshold. High neuron sensitivity to the action of the comparatively weak slow control signals is established. This explains the capability of the neurons to perform flexible tuning of their selective properties for detecting various external signals in sufficiently short times (of the order of duration of several spikes).