000129860 001__ 129860
000129860 005__ 20240112163659.0
000129860 0247_ $$2doi$$a10.1063/5.0043302
000129860 0248_ $$2sideral$$a124657
000129860 037__ $$aART-2021-124657
000129860 041__ $$aeng
000129860 100__ $$0(orcid)0000-0002-5701-1670$$aSerrano, Sergio$$uUniversidad de Zaragoza
000129860 245__ $$aOrder in chaos: Structure of chaotic invariant sets of square-wave neuron models
000129860 260__ $$c2021
000129860 5060_ $$aAccess copy available to the general public$$fUnrestricted
000129860 5203_ $$aBursting phenomena and, in particular, square-wave or fold/hom bursting, are found in a wide variety of mathematical neuron models. These systems have different behavior regimes depending on the parameters, whether spiking, bursting, or chaotic. We study the topological structure of chaotic invariant sets present in square-wave bursting neuron models, first detailed using the Hindmarsh–Rose neuron model and later exemplary in the more realistic model of a leech heart neuron. We show that the unstable periodic orbits that form the skeleton of the chaotic invariant sets are deeply related to the spike-adding phenomena, typical from these models, and how there are specific symbolic sequences and a symbolic grammar that organize how and where the periodic orbits appear. Linking this information with the topological template analysis permits us to understand how the internal structure of the chaotic invariants is modified and how more symbolic sequences are allowed. Furthermore, the results allow us to conjecture that, for these systems, the limit template when the small parameter ¿, which controls the slow gating variable, tends to zero is the complete Smale topological template.
000129860 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17R$$9info:eu-repo/grantAgreement/ES/DGA-FSE/LMP124-18$$9info:eu-repo/grantAgreement/ES/MINECO-FEDER/PGC2018-096026-B-I00$$9info:eu-repo/grantAgreement/ES/MINECO/PID2019-105674RB-I00
000129860 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000129860 590__ $$a3.741$$b2021
000129860 591__ $$aPHYSICS, MATHEMATICAL$$b7 / 56 = 0.125$$c2021$$dQ1$$eT1
000129860 591__ $$aMATHEMATICS, APPLIED$$b17 / 267 = 0.064$$c2021$$dQ1$$eT1
000129860 592__ $$a1.009$$b2021
000129860 593__ $$aApplied Mathematics$$c2021$$dQ1
000129860 593__ $$aStatistical and Nonlinear Physics$$c2021$$dQ1
000129860 593__ $$aPhysics and Astronomy (miscellaneous)$$c2021$$dQ1
000129860 593__ $$aMathematical Physics$$c2021$$dQ1
000129860 594__ $$a5.8$$b2021
000129860 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000129860 700__ $$0(orcid)0000-0002-7374-3222$$aMartínez, M. Ángeles$$uUniversidad de Zaragoza
000129860 700__ $$0(orcid)0000-0002-8089-343X$$aBarrio, Roberto$$uUniversidad de Zaragoza
000129860 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000129860 773__ $$g31, 4 (2021), [25 pp.]$$pChaos$$tCHAOS$$x1054-1500
000129860 8564_ $$s14624879$$uhttps://zaguan.unizar.es/record/129860/files/texto_completo.pdf$$yPostprint
000129860 8564_ $$s1449300$$uhttps://zaguan.unizar.es/record/129860/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000129860 909CO $$ooai:zaguan.unizar.es:129860$$particulos$$pdriver
000129860 951__ $$a2024-01-12-14:08:50
000129860 980__ $$aARTICLE