skip to main content

SciTech ConnectSciTech Connect

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

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.
Authors:
;  [1] ;  [2] ;  [3] ;  [4]
  1. Computational Dynamics Group, Departamento de Matemática Aplicada, GME and IUMA, Universidad de Zaragoza, E-50009 Zaragoza (Spain)
  2. Computational Dynamics Group, GME, Universidad de Zaragoza, E-50009 Zaragoza (Spain)
  3. Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30078 (United States)
  4. (Russian Federation)
Publication Date:
OSTI Identifier:
22351116
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 24; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; DIAGRAMS; EVALUATION; HYSTERESIS; LYAPUNOV METHOD; NERVE CELLS