Geodesic
Qualitative methods for case study of the Hindmarch--Rose model
Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 23-52

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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, dynamics, bistability, tonic spiking, bursting.
Mots-clés : neuron, bifurcations, blue sky catastrophe 
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     author = {M. Kolomiets and A. Shilnikov},
     title = {Qualitative methods for case study of the {Hindmarch--Rose} model},
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     publisher = {mathdoc},
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     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2010_6_1_a1/}
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M. Kolomiets; A. Shilnikov. Qualitative methods for case study of the Hindmarch--Rose model. Russian journal of nonlinear dynamics, Tome 6 (2010) no. 1, pp. 23-52. http://geodesic.mathdoc.fr/item/ND_2010_6_1_a1/