58355 20240122154813.0 doi 10.1063/1.4882171 sideral 89929 ART-2014-89929 eng Barrio Gil, Roberto Universidad de Zaragoza (orcid)0000-0002-8089-343X Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons 2014 Access copy available to the general public Unrestricted Understanding common dynamical principles underlying an abundance of widespread brain behaviors is a pivotal challenge in the new century. The bottom-up approach to the challenge should be based on solid foundations relying on detailed and systematic understanding of dynamical functions of its basic components—neurons—modeled as plausibly within the Hodgkin-Huxley framework as phenomenologically using mathematical abstractions. Such one is the Hindmarsh-Rose (HR) model, reproducing fairly the basic oscillatory activities routinely observed in isolated biological cells and in neural networks. This explains a wide popularity of the HR-model in modern research in computational neuroscience. A challenge for the mathematics community is to provide detailed explanations of fine aspects of the dynamics, which the model is capable of, including its responses to perturbations due to network interactions. This is the main focus of the bifurcation theory exploring quantitative variations and qualitative transformations of a system in its parameter space. We will show how generic homoclinic bifurcations of equilibria and periodic orbits can imply transformations and transitions between oscillatory activity types in this and other bursting models of neurons of the Hodgkin-Huxley type. The article is focused specifically on bifurcation scenarios in neuronal models giving rise to irregular or chaotic spiking and bursting. The article demonstrates how the combined use of several state-of-the-art numerical techniques helps us confine “onion”-like regions in the parameter space, with macro-chaotic complexes as well as micro-chaotic structures occurring near spike-adding bifurcations. info:eu-repo/grantAgreement/ES/DGA/E48 info:eu-repo/grantAgreement/ES/MICINN/MTM2012-31883 info:eu-repo/semantics/openAccess by http://creativecommons.org/licenses/by/3.0/es/ 1.954 2014 PHYSICS, MATHEMATICAL 9 / 54 = 0.167 2014 Q1 T1 MATHEMATICS, APPLIED 17 / 256 = 0.066 2014 Q1 T1 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Martínez Carballo, M. Ángeles (orcid)0000-0002-7374-3222 Serrano Pastor, Sergio Universidad de Zaragoza (orcid)0000-0002-5701-1670 Shilnikov, Andrey 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 24, 2 (2014), 023128 [11 pp] Chaos CHAOS 1054-1500 500830 http://zaguan.unizar.es/record/58355/files/texto_completo.pdf Versión publicada 138684 http://zaguan.unizar.es/record/58355/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:58355 articulos driver 2024-01-22-15:30:58 ARTICLE