000058355 001__ 58355
000058355 005__ 20240122154813.0
000058355 0247_ $$2doi$$a10.1063/1.4882171
000058355 0248_ $$2sideral$$a89929
000058355 037__ $$aART-2014-89929
000058355 041__ $$aeng
000058355 100__ $$0(orcid)0000-0002-8089-343X$$aBarrio Gil, Roberto$$uUniversidad de Zaragoza
000058355 245__ $$aMacro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons
000058355 260__ $$c2014
000058355 5060_ $$aAccess copy available to the general public$$fUnrestricted
000058355 5203_ $$aUnderstanding 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.
000058355 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2012-31883
000058355 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000058355 590__ $$a1.954$$b2014
000058355 591__ $$aPHYSICS, MATHEMATICAL$$b9 / 54 = 0.167$$c2014$$dQ1$$eT1
000058355 591__ $$aMATHEMATICS, APPLIED$$b17 / 256 = 0.066$$c2014$$dQ1$$eT1
000058355 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000058355 700__ $$0(orcid)0000-0002-7374-3222$$aMartínez Carballo, M. Ángeles
000058355 700__ $$0(orcid)0000-0002-5701-1670$$aSerrano Pastor, Sergio$$uUniversidad de Zaragoza
000058355 700__ $$aShilnikov, Andrey
000058355 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000058355 773__ $$g24, 2 (2014), 023128 [11 pp]$$pChaos$$tCHAOS$$x1054-1500
000058355 8564_ $$s500830$$uhttps://zaguan.unizar.es/record/58355/files/texto_completo.pdf$$yVersión publicada
000058355 8564_ $$s138684$$uhttps://zaguan.unizar.es/record/58355/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000058355 909CO $$ooai:zaguan.unizar.es:58355$$particulos$$pdriver
000058355 951__ $$a2024-01-22-15:30:58
000058355 980__ $$aARTICLE