Andrey Shilnikov
10, Ulyanov Str, 603005 Nizhny Novgorod/
750 COE, 7th floor, 30 Pryor Street, 30303-3083, Atlanta, USA
750 COE, 7th floor, 30 Pryor Street, 30303-3083, Atlanta, USA
Department of Differential Equations Research Institute for Applied Mathematics & Cybernetics of Nizhny Novgorod University/
Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia
Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia
Publications:
|
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.
|