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Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2010, Volume 6, Number 1, Pages 23–52
(Mi nd54)
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This article is cited in 2 scientific papers (total in 2 papers)
Qualitative methods for case study of the Hindmarch–Rose model
M. Kolomietsa, A. Shilnikovb a Agricultural Academy
b Department of Mathematics and Statistics, Neuroscience Institute, Georgia State University
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.
Keywords:
Hindmarsh–Rose model, neuron, dynamics, bifurcations, blue sky catastrophe, bistability, tonic spiking, bursting.
Received: 06.12.2009
Citation:
M. Kolomiets, A. Shilnikov, “Qualitative methods for case study of the Hindmarch–Rose model”, Nelin. Dinam., 6:1 (2010), 23–52
Linking options:
https://www.mathnet.ru/eng/nd54 https://www.mathnet.ru/eng/nd/v6/i1/p23
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