Abstract
A new method to model the phenomena 'bursting' and 'buffering' in neural systems is represented. Namely, a singularly perturbed nonlinear scalar differential difference 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 buffering phenomenon occurs in a one-dimensional chain of diffusively coupled neurons of this type: as the number of components in the chain grows in a way compatible with a decrease of the diffusion coefficient, the number of co-existing stable periodic motions increases indefinitely.
Export citation and abstract BibTeX RIS
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.