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This master\u2013slave configuration features neuron N1 as the master, subjected to an external sinusoidal electrical current, and neuron N2 as the slave, interacting with N1 through an electrical force. We report numerical results for three distinct scenarios where N1 operates in (i) periodic, (ii) quasiperiodic, and (iii) chaotic regimes. The primary objective is to explore how the dynamics of the master neuron N1 influence the coupled system\u2019s behavior. To achieve this, we generated cross sections of the seven-dimensional parameter space, known as parameter planes. Our findings reveal that in the periodic regime of N1, the coupled system exhibits period-adding sequences of Arnold tongue-like structures in the parameter planes. Furthermore, regions of multistability can also be identified in these parameter planes of the coupled system. In the quasiperiodic regime, regions of periodic motion are absent, with only regions of quasiperiodic and chaotic dynamics present. In the chaotic regime of N1, the parameter planes display regions of chaos, hyperchaos, and transient hyperchaos.<\/jats:p>","DOI":"10.1063\/5.0219640","type":"journal-article","created":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T16:21:39Z","timestamp":1726762899000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Influence of sinusoidal forcing on the master FitzHugh\u2013Nagumo neuron model and global dynamics of a unidirectionally coupled two-neuron system"],"prefix":"10.1063","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7433-0384","authenticated-orcid":false,"given":"N\u00edvea D.","family":"Bosco","sequence":"first","affiliation":[{"name":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina 1 , 89219-710 Joinville, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2235-0469","authenticated-orcid":false,"given":"Paulo C.","family":"Rech","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade do Estado de Santa Catarina 1 , 89219-710 Joinville, 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":"Departamento de F\u00edsica, Universidade Federal do Paran\u00e1 2 , 81531-980 Curitiba, 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 1 , 89219-710 Joinville, Brazil"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2024,9,19]]},"reference":[{"key":"2024091915551965300_c1","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1016\/j.neuron.2006.09.020","article-title":"Neural synchrony in brain disorders: Relevance for cognitive dysfunctions and pathophysiology","volume":"52","year":"2006","journal-title":"Neuron"},{"key":"2024091915551965300_c2","volume-title":"Mathematical Foundations of Neuroscience","year":"2010"},{"key":"2024091915551965300_c3","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1038\/35067550","article-title":"The brainweb: Phase synchronization and large-scale integration","volume":"2","year":"2001","journal-title":"Nat. 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