{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T09:54:31Z","timestamp":1781603671137,"version":"3.54.5"},"reference-count":89,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T00:00:00Z","timestamp":1781136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We show that a single Hodgkin\u2013Huxley (HH) neuron with Pyragas-type delayed feedback control (DFC) can store multiple symbols as stable periodic orbits, where the specific orbit is selected by tuning the DFC gain K and time delay \u03c4. Sweeping the (K,\u03c4) parameter plane at fixed bias current Ibias = 10.0 \u03bcA\/cm2 reveals 207 orbit types across 12 topological categories, with inter-spike interval (ISI) means from 5.9 to 56.9 ms. We establish: (i) a write protocol that reliably locks orbits with 13.9 ms median settling time; (ii) a novel Pattern-Oriented Limit-cycle Decoder (POLD) that reads orbits at 100% accuracy from only five observed ISIs (1200 trials across 12 orbits; Wilson 95% CI: 99.7\u2013100%); (iii) a complete single-symbol write\u2013read\u2013erase (W\u2013R\u2013E) cycle with 100% read accuracy, 92% erase verification, and no decay over hold durations up to 50 s; and (iv) a fully validated 12-symbol memory capacity with a read-discriminable upper bound of 67 symbols (11.2\u00d7 over rate coding; write viability confirmed only for the conservative 12-symbol subset). Reliable orbit addressing needs delay precision of \u00b12%, which constitutes a write-precision specification and not a fundamental capacity limit. These findings show that parametric delayed feedback is a viable mechanism for limit-cycle-based information storage in conductance-based spiking neurons. The biological interpretation is analogical, not direct: the \u00b12% delay-precision requirement exceeds what has been demonstrated for biological autaptic variability, and the orbit-coded memory framing is best understood as a computational proof-of-principle aimed at neuromorphic engineering, not as a claim about biological working memory.<\/jats:p>","DOI":"10.3390\/e28060678","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T09:06:52Z","timestamp":1781600812000},"page":"678","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Limit-Cycle Proliferation Under Parametric Delayed Feedback in a Conductance-Based Neuron: Bifurcation Landscape, Orbit Catalog, and Capacity Analysis"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2608-6573","authenticated-orcid":false,"given":"Mohammad O.","family":"Alhawarat","sequence":"first","affiliation":[{"name":"Faculty of Information Technology, Al-Ahliyya Amman University, Amman 19328, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9169-6442","authenticated-orcid":false,"given":"Ayman J.","family":"Alnsour","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Al-Ahliyya Amman University, Amman 19328, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3554-3614","authenticated-orcid":false,"given":"Mohammed A. F.","family":"Al-Husainy","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Al-Ahliyya Amman University, Amman 19328, Jordan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4170-0751","authenticated-orcid":false,"given":"Khalil M.","family":"Abdelnaby","sequence":"additional","affiliation":[{"name":"Faculty of Information Technology, Al-Ahliyya Amman University, Amman 19328, Jordan"},{"name":"Systems and Computers Engineering Department, Faculty of Engineering, Al-Azhar University, Nasr City, Cairo 11765, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1016\/0959-4388(94)90059-0","article-title":"Noise, neural codes and cortical organization","volume":"4","author":"Shadlen","year":"1994","journal-title":"Curr. Opin. 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