Self-sustained relaxation oscillations in time-delay neural systemsстатья
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Дата последнего поиска статьи во внешних источниках: 2 декабря 2016 г.
Аннотация:A new method to model the phenomena 'bursting' and 'buering' in neural systems is represented. Namely, a singularly perturbed nonlinear scalar dierential dierence equation with two delays is introduced, which is a mathematical model of a single neuron. It is shown that for suitably chosen parameters this equation has a stable periodic solution with an arbitrary prescribed number of asymptotically high impulses (spikes) on a period interval. It is also shown that the buering phenomenon occurs in a one-dimensional chain of diusively coupled neurons of this type: as the number of components in the chain grows in a way compatible with a decrease of the diusion coecient, the number of co-existing stable periodic motions increases indenitely.