{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:30:12Z","timestamp":1760239812977,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,12,27]],"date-time":"2020-12-27T00:00:00Z","timestamp":1609027200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations\u2014realizable by a rather simple electronic circuit\u2014capable of producing a generalized attracting horseshoe map. A system specifically designed to have a Poincar\u00e9 section yielding the desired map is described, but not pursued due to its complexity, which makes the construction of a circuit realization exceedingly difficult. Instead, the generalized attracting horseshoe and its trapping region is obtained by using a carefully chosen Poincar\u00e9 map of the R\u00f6ssler attractor. Novel numerical techniques are employed to iterate the map of the trapping region to approximate the chaotic strange attractor contained in the generalized attracting horseshoe, and an electronic circuit is constructed to produce the map. Several potential applications of the idea of a generalized attracting horseshoe and a physical electronic circuit realization are proposed.<\/jats:p>","DOI":"10.3390\/sym13010030","type":"journal-article","created":{"date-parts":[[2020,12,27]],"date-time":"2020-12-27T20:52:21Z","timestamp":1609102341000},"page":"30","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Generalized Attracting Horseshoe in the R\u00f6ssler Attractor"],"prefix":"10.3390","volume":"13","author":[{"given":"Karthik","family":"Murthy","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, IL 61801, USA"}]},{"given":"Ian","family":"Jordan","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA"}]},{"given":"Parth","family":"Sojitra","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA"}]},{"given":"Aminur","family":"Rahman","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3524-9538","authenticated-orcid":false,"given":"Denis","family":"Blackmore","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,27]]},"reference":[{"key":"ref_1","unstructured":"Carins, S. (1963). Diffeomorphisms with many periodic points. Differential and Combinatorial Topology, Princeton University Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2","article-title":"Deterministic nonperiodic flow","volume":"20","author":"Lorenz","year":"1963","journal-title":"J. Atoms. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/0375-9601(76)90101-8","article-title":"An equation for continuous chaos","volume":"57","year":"1976","journal-title":"Phys. Lett. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1055","DOI":"10.1109\/TCS.1984.1085459","article-title":"A chaotic attractor from Chua\u2019s circuit","volume":"31","author":"Matsumoto","year":"1984","journal-title":"IEEE Trans. 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Generalized attracting horseshoe and chaotic strange attractors. arXiv."},{"key":"ref_9","first-page":"1","article-title":"Qualitative models and experimental investigation of chaotic nor gates and set\/reset flip-flops","volume":"474","author":"Rahman","year":"2018","journal-title":"Proc. Roy. Soc. A"},{"key":"ref_10","unstructured":"Gonze, D. (2011, February 25). poincare.m. Available online: http:\/\/homepages.ulb.ac.be\/~dgonze\/info\/matlab\/poincare.m."},{"key":"ref_11","unstructured":"Glen, K. (2017, January 25). Rossler Attractor. Available online: http:\/\/www.glensstuff.com\/rosslerattractor\/rossler.htm."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:46:34Z","timestamp":1760179594000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,27]]},"references-count":11,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010030"],"URL":"https:\/\/doi.org\/10.3390\/sym13010030","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2020,12,27]]}}}