{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T01:33:48Z","timestamp":1787276028674,"version":"build-2736575974"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"10","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,10]]},"abstract":"<jats:p> The transition from periodicity to chaos in a DC-DC Buck power converter is studied in this paper. The converter is controlled through a direct Pulse Width Modulation (PWM) in order to regulate the error dynamics at zero. Results show robustness with low output error and a fixed switching frequency. Furthermore, some rich dynamics appear as the constant associated with the first-order error dynamics decreases. Finally, a transition from periodicity to chaos is observed. This paper describes this transition and the bifurcations in the converter. Chaos appears in the system with a stretching and folding mechanism. It can be observed in the one-dimensional Poincar\u00e9 map of the inductor current. This Poincar\u00e9 map converges to a tent map with the variation of the system parameter k<jats:sub>s<\/jats:sub>. <\/jats:p>","DOI":"10.1142\/s0218127405014015","type":"journal-article","created":{"date-parts":[[2005,12,22]],"date-time":"2005-12-22T05:26:18Z","timestamp":1135229178000},"page":"3245-3264","source":"Crossref","is-referenced-by-count":32,"title":["TRANSITION FROM PERIODICITY TO CHAOS IN A PWM-CONTROLLED BUCK CONVERTER WITH ZAD STRATEGY"],"prefix":"10.1142","volume":"15","author":[{"given":"FABIOLA","family":"ANGULO","sequence":"first","affiliation":[{"name":"Universidad Nacional de Colombia, Cra 27 No. 64-60, Manizales, Colombia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ENRIC","family":"FOSSAS","sequence":"additional","affiliation":[{"name":"Technical University of Catalonia, Advanced Control of Energy Systems, Institute of Industrial and Control Engineering, Avda. Diagonal 647, pl 11, 08027 Barcelona, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"GERARD","family":"OLIVAR","sequence":"additional","affiliation":[{"name":"Technical University of Catalonia, Advanced Control of Energy Systems, EPSEVG and FME Avda. Victor Balaguer, s\/n, 08800 Vilanova i la Geltr\u00fa, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/81.622992"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1109\/63.662832"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.59.4052"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/9780470545393"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1109\/63.491637"},{"key":"rf12","first-page":"1129","volume":"44","author":"Deane J. H. B.","journal-title":"IEEE Trans. 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