Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons

Chaos. 2014 Jun;24(2):023128. doi: 10.1063/1.4882171.

Abstract

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. Such an aggregated approach allows for detecting regions of simple and chaotic dynamics, and demarcating borderlines-exact bifurcation curves. 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 of onion bulb shapes and revealing spike-adding cascades that generate micro-chaotic structures due to the hysteresis.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Action Potentials / physiology*
  • Models, Neurological*
  • Neurons / physiology*
  • Nonlinear Dynamics*
  • Numerical Analysis, Computer-Assisted