{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T02:29:12Z","timestamp":1749090552593},"reference-count":24,"publisher":"World Scientific Pub Co Pte Ltd","issue":"09","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p> In this work a thorough study is presented of the bifurcation structure of an embedding of one-dimensional Allee\u2019s functions into a two-dimensional diffeomorphism. A complete classification of the nature and stability of the fixed points, on the contour lines of the two-dimensional diffeomorphism, is provided. A necessary and sufficient condition so that the Allee fixed point is a snapback repeller is established. Sufficient conditions for the occurrence of homoclinic tangencies of a saddle fixed point of the two-dimensional diffeomorphism are also established, associated to the snapback repeller bifurcation of the endomorphism defined by the Allee functions. The main results concern homoclinic and big bang bifurcations of the diffeomorphism as \u201cgerminal\u201d bifurcations of the Allee functions. Our results confirm previous predictions of structures of homoclinic and big bang bifurcation curves in dimension one and extend these studies to \u201clocal\u201d concepts of Allee effect and big bang bifurcations to this two-dimensional exponential diffeomorphism. <\/jats:p>","DOI":"10.1142\/s0218127417300300","type":"journal-article","created":{"date-parts":[[2017,9,10]],"date-time":"2017-09-10T23:15:58Z","timestamp":1505085358000},"page":"1730030","source":"Crossref","is-referenced-by-count":15,"title":["Homoclinic and Big Bang Bifurcations of an Embedding of 1D Allee\u2019s Functions into a 2D Diffeomorphism"],"prefix":"10.1142","volume":"27","author":[{"given":"J. Leonel","family":"Rocha","sequence":"first","affiliation":[{"name":"ADM, ISEL-Instituto Sup. de Engenharia de Lisboa, Instituto Polit\u00e9cnico de Lisboa, Rua Conselheiro Em\u00eddio Navarro 1, 1959-007 Lisboa, Portugal"}]},{"given":"Abdel-Kaddous","family":"Taha","sequence":"additional","affiliation":[{"name":"INSA, University of Toulouse, 135 Avenue de Rangueil, 31077 Toulouse, France"}]},{"given":"D.","family":"Fournier-Prunaret","sequence":"additional","affiliation":[{"name":"LAAS-CNRS, INSA, University of Toulouse, 7 Avenue du Colonel Roche, 31077 Toulouse, France"}]}],"member":"219","published-online":{"date-parts":[[2017,9,10]]},"reference":[{"key":"S0218127417300300BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127493000763"},{"key":"S0218127417300300BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(95)00185-X"},{"key":"S0218127417300300BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127400001900"},{"key":"S0218127417300300BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000616"},{"key":"S0218127417300300BIB005","first-page":"525","volume":"293","author":"El-Hamouly H.","year":"1982","journal-title":"C. R. Acad. Sci. Paris"},{"key":"S0218127417300300BIB006","first-page":"253","volume":"298","author":"Fournier-Prunaret D.","year":"1984","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r 1"},{"key":"S0218127417300300BIB007","first-page":"223","volume":"301","author":"Fournier-Prunaret D.","year":"1985","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r 1"},{"key":"S0218127417300300BIB008","first-page":"325","volume":"301","author":"Fournier-Prunaret D.","year":"1985","journal-title":"C. R. Acad. Sci. Paris, S\u00e9r 1"},{"key":"S0218127417300300BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/0362-546X(94)90198-8"},{"key":"S0218127417300300BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2011.03.004"},{"volume-title":"Dynamique Chaotique","year":"1980","author":"Gumowski I.","key":"S0218127417300300BIB011"},{"key":"S0218127417300300BIB012","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1984.0020"},{"key":"S0218127417300300BIB013","doi-asserted-by":"publisher","DOI":"10.1142\/0413"},{"key":"S0218127417300300BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-58031-4_3"},{"key":"S0218127417300300BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/2252"},{"key":"S0218127417300300BIB016","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403007631"},{"key":"S0218127417300300BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-29503-4_13"},{"volume-title":"Homoclinic Bifurcations and Hyperbolic Dynamics","year":"1987","author":"Palis J.","key":"S0218127417300300BIB018"},{"key":"S0218127417300300BIB019","doi-asserted-by":"publisher","DOI":"10.1080\/1023619021000047752"},{"key":"S0218127417300300BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1415-0"},{"key":"S0218127417300300BIB021","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2015.20.3131"},{"key":"S0218127417300300BIB022","first-page":"2377","volume":"9","author":"Rocha J. L.","year":"2015","journal-title":"Appl. Math. Inf. Sci."},{"key":"S0218127417300300BIB023","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416300305"},{"key":"S0218127417300300BIB024","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416300305"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417300300","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:48:37Z","timestamp":1565185717000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417300300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8]]},"references-count":24,"journal-issue":{"issue":"09","published-online":{"date-parts":[[2017,9,10]]},"published-print":{"date-parts":[[2017,8]]}},"alternative-id":["10.1142\/S0218127417300300"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417300300","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2017,8]]}}}