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    M. Kolomiets

    97, Gagarina st., Nizhnii Novgorod, 603107, Russia
    Nizhnii Novgorod State Agricultural Academy


    Kolomiets M. L., Shilnikov A. L.
    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
    Citation: Kolomiets M. L., Shilnikov A. L.,  Qualitative methods for case study of the Hindmarch–Rose model, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 1, pp.  23-52

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