{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:31:44Z","timestamp":1723242704994},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,2]]},"abstract":"<jats:p> Alternate quadratic systems [Formula: see text] <\/jats:p><jats:p> where [Formula: see text] and [Formula: see text] are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram (\u201chidden\u201d because it is not visible at normal resolution and \u201cnonstandard\u201d because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A. <\/jats:p>","DOI":"10.1142\/s021812741650036x","type":"journal-article","created":{"date-parts":[[2016,3,9]],"date-time":"2016-03-09T22:26:20Z","timestamp":1457562380000},"page":"1650036","source":"Crossref","is-referenced-by-count":3,"title":["Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System"],"prefix":"10.1142","volume":"26","author":[{"given":"G.","family":"Pastor","sequence":"first","affiliation":[{"name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"}]},{"given":"M.","family":"Romera","sequence":"additional","affiliation":[{"name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"}]},{"given":"M.-F.","family":"Danca","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Emanuel University of Oradea, 410597 Oradea, Rom\u00e2nia"},{"name":"Romanian Institute of Science and Technology, Cire\u015filor 29, Cluj-Napoca, 400487, Rom\u00e2nia"}]},{"given":"A.","family":"Martin","sequence":"additional","affiliation":[{"name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"}]},{"given":"A. B.","family":"Orue","sequence":"additional","affiliation":[{"name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"}]},{"given":"F.","family":"Montoya","sequence":"additional","affiliation":[{"name":"Instituto de Tecnolog\u00edas F\u00edsicas y de la Informaci\u00f3n (ITEFI), Consejo Superior de Investigaciones Cient\u00edficas (CSIC), Serrano 144, Madrid 28006, Spain"}]},{"given":"L. 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