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 Title Describing chaotic structures in the Hindmarsh-Rose model of bursting neurons
 Name Roberto Barrio Country Spain Email rbarrio@unizar.es Co-Author(s) M. Angeles Martinez, Sergio Serrano, Marc Lefranc and Andrey Shilnikov Submit Time 2014-02-26 08:51:08 Session Special Session 112: Nonlinear dynamics in neuroscience
 Contents In this talk we study a plethora of chaotic phenomena in the Hindmarsh-Rose neuron model with the use of several computational techniques including the bifurcation parameter continuation, spike-quantification and evaluation of Lyapunov exponents in bi-parameter diagrams. We demonstrate how the organizing centers -- points corresponding to codimension-two homoclinic bifurcations -- along with fold and period-doubling bifurcation curves structure the biparametric plane, thus forming macro-chaotic regions resembling onion bulb scales'' and revealing spike-adding cascades that generate micro-chaotic structures due to the hysteresis. Moreover, we describe the topological changes in the structure of the chaotic attractors and their influence in the system.