M. Kolomiets
97, Gagarina st., Nizhnii Novgorod, 603107, Russia
Nizhnii Novgorod State Agricultural Academy
Publications:
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Kolomiets M. L., Shilnikov A. L.
Qualitative methods for case study of the Hindmarch–Rose model
2010, Vol. 6, No. 1, pp. 23-52
Abstract
We demonstrate that bifurcations of periodic orbits underlie the dynamics of the Hindmarsh–Rose model and other square-wave bursting models of neurons of the Hodgkin–Huxley type. Such global bifurcations explain in-depth the transitions between the tonic spiking and bursting oscillations in a model.We show that a modified Hindmarsh-Rose model can exhibit the blue sky bifurcation, and a bistability of the coexisting tonic spiking and bursting activities.
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