{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,24]],"date-time":"2023-08-24T10:21:08Z","timestamp":1692872468673},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,9]]},"abstract":"<jats:p> Ten years ago, Dixon et al. [1993] studied the behavior of a continuous-time system displaying erratic, apparently chaotic, dynamics. This is a paradoxical case since the system is two-dimensional, which is seemingly a violation of the Poincare\u2013Bendixon theorem. Using numerical studies, Dixon et al. explained such a behavior from the presence of an attracting singularity, which induces arbitrarily large sensitivity to initial conditions. The aim of this letter is to use singularity regularization techniques to study the dynamics around the system singularity. The results obtained in this way explain the paradoxical situation of having continuous \"chaotic\" dynamics in a two-dimensional system. <\/jats:p>","DOI":"10.1142\/s021812740501385x","type":"journal-article","created":{"date-parts":[[2005,10,26]],"date-time":"2005-10-26T11:55:00Z","timestamp":1130327700000},"page":"3023-3029","source":"Crossref","is-referenced-by-count":4,"title":["THE ORIGIN OF A CONTINUOUS TWO-DIMENSIONAL \"CHAOTIC\" DYNAMICS"],"prefix":"10.1142","volume":"15","author":[{"given":"JOSE","family":"ALVAREZ-RAMIREZ","sequence":"first","affiliation":[{"name":"Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Iztapalapa, D. F., 09340, Mexico"}]},{"given":"JOAQUIN","family":"DELGADO-FERNANDEZ","sequence":"additional","affiliation":[{"name":"Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Iztapalapa, D. F., 09340, Mexico"}]},{"given":"GILBERTO","family":"ESPINOSA-PAREDES","sequence":"additional","affiliation":[{"name":"Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Iztapalapa, D. F., 09340, Mexico"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1086\/171007"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01403170"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90008-O"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/28\/19\/010"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01390175"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812740501385X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:09:42Z","timestamp":1565136582000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812740501385X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9]]},"references-count":5,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,9]]}},"alternative-id":["10.1142\/S021812740501385X"],"URL":"https:\/\/doi.org\/10.1142\/s021812740501385x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,9]]}}}