{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T13:44:55Z","timestamp":1791812695020,"version":"4.3.4"},"reference-count":8,"publisher":"AIP Publishing","issue":"10","funder":[{"DOI":"10.13039\/501100001843","name":"Anusandhan National Research Foundation","doi-asserted-by":"publisher","award":["CRG\/2022\/001541"],"award-info":[{"award-number":["CRG\/2022\/001541"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,10,1]]},"abstract":"<jats:p>In their paper, Linage et al. [Phys. Lett. A 359, 638\u2013639 (2006)] reported the appearance of Fibonacci ordering in the Feigenbaum scaling of the period-doubling cascade to chaos. Although their results demonstrated this connection numerically (verifying up to the 22nd term), the theoretical origin of the Fibonacci sequence in this context was not fully developed. Here, we provide a theoretical explanation showing that Fibonacci ordering arises naturally from the combinatorial structure of branching generated by period-doubling cascading. This provides the theoretical connection between the period-doubling route to chaos and the Fibonacci sequence.<\/jats:p>","DOI":"10.1063\/5.0353533","type":"journal-article","created":{"date-parts":[[2026,10,12]],"date-time":"2026-10-12T12:46:45Z","timestamp":1791809205000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Explaining the Fibonacci order in the period-doubling cascade to chaos"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0057-1394","authenticated-orcid":false,"given":"Aarsh","family":"Chotalia","sequence":"first","affiliation":[{"name":"Department of Physics, Indian Institute of Technology Bombay , Mumbai 400076,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5410-5148","authenticated-orcid":false,"given":"P.","family":"Parmananda","sequence":"additional","affiliation":[{"name":"Department of Physics, Indian Institute of Technology Bombay , Mumbai 400076,","place":["India"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,12]]},"reference":[{"key":"2026101208463632800_c1","doi-asserted-by":"crossref","unstructured":"T.\n            N\u00e9gadi\n          , \u201cA mathematical model for the genetic code(s) based on Fibonacci numbers and their q-analogues,\u201d arXiv:1510.01278 (2015).","DOI":"10.14704\/nq.2015.13.3.850"},{"key":"2026101208463632800_c2","doi-asserted-by":"publisher","first-page":"1936","DOI":"10.4236\/jamp.2022.106133","article-title":"Fibonacci stoichiometry and superb performance of Nb16W5O55 and related super-battery materials","volume":"10","year":"2022","journal-title":"J. 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