Qualitative methods for case study of the Hindmarch–Rose model

    2010, Vol. 6, No. 1, pp.  23-52

    Author(s): 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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