{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:20:50Z","timestamp":1753874450459,"version":"3.41.2"},"reference-count":36,"publisher":"AIP Publishing","issue":"11","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,11,1]]},"abstract":"<jats:p>This paper reports the first finding of cupolets in a chaotic Hindmarsh\u2013Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme by applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh\u2013Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The type of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory by a perturbation determined by the coding function rN(x). We report the discovery of many cupolets with corresponding control sequences and comment on the differences with previously reported cupolets in the double scroll system. We provide some examples of the generated cupolets and conclude by discussing potential implications for biological neurons.<\/jats:p>","DOI":"10.1063\/5.0101667","type":"journal-article","created":{"date-parts":[[2022,11,2]],"date-time":"2022-11-02T18:44:32Z","timestamp":1667414672000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":2,"title":["Cupolets in a chaotic neuron model"],"prefix":"10.1063","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1407-4356","authenticated-orcid":false,"given":"John E.","family":"Parker","sequence":"first","affiliation":[{"name":"Integrated Applied Mathematics Program, Department of Mathematics and Statistics, University of New Hampshire , Durham, New Hampshire 03824, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1624-5892","authenticated-orcid":false,"given":"Kevin M.","family":"Short","sequence":"additional","affiliation":[{"name":"Integrated Applied Mathematics Program, Department of Mathematics and Statistics, University of New Hampshire , Durham, New Hampshire 03824, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2022,11,2]]},"reference":[{"key":"2023080921192788400_c1","doi-asserted-by":"publisher","first-page":"1063","DOI":"10.1109\/TNN.2004.832719","article-title":"Which model to use for cortical spiking neurons?","volume":"15","year":"2004","journal-title":"IEEE Trans. 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