title: Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons.
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.
authors.affiliation: Computational Dynamics Group, Departamento de Matemática Aplicada, GME and IUMA, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
authors.forename: Roberto
authors.initials: R
authors.lastname: Barrio
authors.affiliation: Computational Dynamics Group, GME, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
authors.forename: M Angeles
authors.initials: MA
authors.lastname: Martínez
authors.affiliation: Computational Dynamics Group, Departamento de Matemática Aplicada, GME and IUMA, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
authors.forename: Sergio
authors.initials: S
authors.lastname: Serrano
authors.affiliation: Neuroscience Institute and Department of Mathematics and Statistics, Georgia State University, Atlanta, Georgia 30078, USA.
authors.forename: Andrey
authors.initials: A
authors.lastname: Shilnikov
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted