{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T15:03:47Z","timestamp":1789398227278,"version":"build-2803163510"},"reference-count":77,"publisher":"AIP Publishing","issue":"9","funder":[{"name":"Natural Science foundation of China Shengdu"}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2026,9,1]]},"abstract":"<jats:p>Toroidal chaos designates a chaotic solution that is structured in the neighborhood of a torus. For being chaotic, such a torus needs to be discontinuously fractalized to present a Cantor set, ensuring the great sensitivity to initial conditions required for chaos. A fractal is related to self-similarity and a non-integer dimension. In fact, although clearly introduced as such by Mandelbrot, it was never written in a paper related to strange nonchaotic attractors that an object can be fractal in two very different ways: under a continuous way, as a coastline, or in a discontinuous way, as a Cantor set. If the latter is necessarily related to chaos, the former can, for instance, be associated with a continuous torus fractalization leading to a strange nonchaotic attractor. Moreover, although being fractal, the torus is still regular and, consequently, a strange nonchaotic attractor is a particular type of quasiperiodic attractor. We will, therefore, focus on showing with the help of three different cases\u2014produced by two coupled van der Pol oscillators or by a quasiperiodically driven Duffing system, that the fractalization is actually continuous when strange nonchaotic attractors are observed. In one of the cases, it will be shown that the largest Lyapunov exponent wrongly suggests chaos rather than a strange nonchaotic attractor. We also investigate how, in the presence of symmetry, an attractor merging crisis-induced intermittency can be observed, just after two symmetry-related strange nonchaotic attractors.<\/jats:p>","DOI":"10.1063\/5.0354681","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T14:11:19Z","timestamp":1789395079000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Continuously pleated torus or strange nonchaotic attractors seen as continuously fractalized quasiperiodic attractors"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3603-394X","authenticated-orcid":false,"given":"Christophe","family":"Letellier","sequence":"first","affiliation":[{"name":"Department of Physics, Universit\u2019e de Rouen Normandie 1 , Avenue de l\u2019Universit\u2019e, 76800 Saint-Etienne du Rouvray,","place":["France"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4781-0567","authenticated-orcid":false,"given":"Nataliya","family":"Stankevich","sequence":"additional","affiliation":[{"name":"Laboratory of Topological Methods in Dynamics, National Research University Higher School of Economics 2 , Bolshaya Pecherskaya str., 25\/12, Nizhny Novgorod 603155,","place":["Russia"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2733-1366","authenticated-orcid":false,"given":"Samer","family":"Houri","sequence":"additional","affiliation":[{"name":"IMEC 3 , Leuven,","place":["Belgium"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2532-1674","authenticated-orcid":false,"given":"Ludovico","family":"Minati","sequence":"additional","affiliation":[{"name":"School of Life Science and Technology, University of Electronic Science and Technology of China 4 , 611731 Chengdu, Sishuan,","place":["China"]},{"name":"International Research Center of Complexity Sciences, Hangzhou International Innovation Institute, Beihang University, 311115 Hangzhou 5 ,","place":["China"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,9,14]]},"reference":[{"key":"2026091410111177700_c1","doi-asserted-by":"publisher","first-page":"1168","DOI":"10.1515\/zna-1976-1006","article-title":"Chemical turbulence: Chaos in a simple reaction-diffusion system","volume":"31","year":"1976","journal-title":"Z. 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