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High-resolution Lyapunov diagrams with local-maxima (LM) classification expose a hierarchical network of Arnold tongues in parameter space. Frequency-locking regions emerge from quasiperiodic dynamics and extend into chaotic domains, following a period-adding organization consistent with Farey-tree ordering. Successive magnifications reveal multiscale embeddings of stable periodic structures containing quint points, where five periodic domains coalesce and satisfy local LM-adding relations. Basin-of-attraction analysis confirms multistability, including coexistence of periodic and chaotic attractors. In a neurostimulation context, these results show that periodic forcing can induce multiple coexisting frequency-locked firing regimes with distinct LM counts, providing a dynamical basis for stimulus-dependent neural encoding and selective response modulation.<\/jats:p>","DOI":"10.1063\/5.0330457","type":"journal-article","created":{"date-parts":[[2026,9,21]],"date-time":"2026-09-21T12:53:15Z","timestamp":1789995195000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Hierarchical frequency-locking organization and quint points in a periodically driven FitzHugh\u2013Nagumo neuron model"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7433-0384","authenticated-orcid":false,"given":"Nivea D.","family":"Bosco","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina (UDESC) 1 , Joinville 89219-710, Santa Catarina,","place":["Brazil"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-6384-6532","authenticated-orcid":false,"given":"Fabio S.","family":"Ramos","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina (UDESC) 1 , Joinville 89219-710, Santa Catarina,","place":["Brazil"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0889-434X","authenticated-orcid":false,"given":"Marcus W.","family":"Beims","sequence":"additional","affiliation":[{"name":"Centro Interdisciplinar de Ci\u00eancia, Tecnologia e Inova\u00e7\u00e3o (CICTI), N\u00facleo de Modelagem e Computa\u00e7\u00e3o Cient\u00edfica (NMCC), e Laboratorio Chaomplexity, Universidade Federal do Paran\u00e1 (UFPR) 2 , Curitiba 81531-980, Paran\u00e1,","place":["Brazil"]},{"name":"Departamento de F\u00edsica, Universidade Federal do Paran\u00e1 (UFPR) 3 , Curitiba 81531-980, Paran\u00e1,","place":["Brazil"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8786-3893","authenticated-orcid":false,"given":"Cesar","family":"Manchein","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina (UDESC) 1 , Joinville 89219-710, Santa Catarina,","place":["Brazil"]},{"name":"Centro Interdisciplinar de Ci\u00eancia, Tecnologia e Inova\u00e7\u00e3o (CICTI), N\u00facleo de Modelagem e Computa\u00e7\u00e3o Cient\u00edfica (NMCC), e Laboratorio Chaomplexity, Universidade Federal do Paran\u00e1 (UFPR) 2 , Curitiba 81531-980, Paran\u00e1,","place":["Brazil"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,21]]},"reference":[{"key":"2026092108530862400_c1","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1016\/j.crvi.2003.09.011","article-title":"Is there chaos in the brain? 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