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    Andrey Shilnikov

    10, Ulyanov Str, 603005 Nizhny Novgorod/
    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


    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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