{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T11:53:44Z","timestamp":1775476424006,"version":"3.50.1"},"reference-count":39,"publisher":"World Scientific Pub Co Pte Ltd","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2019,12,30]]},"abstract":"<jats:p> In this work, we consider a continuous two-dimensional piecewise linear family of maps in which the fixed point and other cycles undergo a center bifurcation, the analogue of a Neimark\u2013Sacker bifurcation, which has a particular structure when occurring in piecewise linear maps. Our goal is to determine and characterize the occurrence of a center bifurcation of supercritical or subcritical type. We show that for the fixed point, a determinant role is played by the virtual fixed point of the system. Also for other [Formula: see text]-cycles the virtual fixed point plays a determinant role, as well as the saddle cycles related to the cycle which undergoes a center bifurcation. A particular bifurcation point separating the two transitions, supercritical and subcritical, is related to a conservative system (the analogue of the Chenciner point in smooth maps). <\/jats:p>","DOI":"10.1142\/s0218127419300416","type":"journal-article","created":{"date-parts":[[2019,12,26]],"date-time":"2019-12-26T04:36:48Z","timestamp":1577335008000},"page":"1930041","source":"Crossref","is-referenced-by-count":8,"title":["Role of the Virtual Fixed Point in the Center Bifurcations in a Family of Piecewise Linear Maps"],"prefix":"10.1142","volume":"29","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3386-6543","authenticated-orcid":false,"given":"Laura","family":"Gardini","sequence":"first","affiliation":[{"name":"Department DESP, University of Urbino, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9852-0391","authenticated-orcid":false,"given":"Wirot","family":"Tikjha","sequence":"additional","affiliation":[{"name":"Faculty of Science and Technology, Pibulsongkram Rajabhat University, Phitsanulok 65000, Thailand"},{"name":"Centre of Excellence in Mathematics, PERDO, CHE, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,12,26]]},"reference":[{"key":"S0218127419300416BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127497000236"},{"key":"S0218127419300416BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2010.02.015"},{"key":"S0218127419300416BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416300408"},{"key":"S0218127419300416BIB004","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.80.3049"},{"key":"S0218127419300416BIB005","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.4052"},{"key":"S0218127419300416BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/9780470545393"},{"key":"S0218127419300416BIB007","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/44\/30\/305101"},{"key":"S0218127419300416BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01207252"},{"key":"S0218127419300416BIB009","volume-title":"Nonsmooth Mechanics Models, Dynamics and Control","author":"Brogliato B.","year":"1999"},{"key":"S0218127419300416BIB010","volume-title":"Epidemic Modelling: An Introduction","author":"Cannings C.","year":"2005"},{"key":"S0218127419300416BIB011","first-page":"965","volume":"2006","author":"Cull P.","year":"2006","journal-title":"Sci. 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