Display Abstract

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
Special Session 112: Nonlinear dynamics in neuroscience
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.