{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:12:36Z","timestamp":1753888356795,"version":"3.41.2"},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,8,14]],"date-time":"2021-08-14T00:00:00Z","timestamp":1628899200000},"content-version":"vor","delay-in-days":225,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Intensive and repetitive simulations are required to study static and dynamic behaviours of systems. Particular phenomena such as bifurcation and chaos require long simulation times and analysis. To check the existence of bifurcations and chaos in a dynamic system, a fine\u2010tuning procedure of a bifurcation parameter is to be carried out. This increases considerably the computing time, and a great amount of patience is needed to obtain adequate results. Because of the high switching frequency of a boost inverter, the integration process of the dynamic model used to describe it uses an integration step that is in general less than one microsecond. This makes the integration process time consuming even for a short simulation. Thus, a fast, but accurate, method is suitable to analyse the dynamic behaviour of the converter. This work contains two topics. First, we develop a like\u2010discrete integration process that permits precise results in a very fast manner. For one switching period, we compute only two or a maximum of three breaking points depending on whether we treat a continuous conduction mode (CCM) or a discontinuous conduction mode (DCM) of the inductor current. Furthermore, with each segment of the dynamic trajectory, an exact analytic formula is associated. The second goal is to use this result to develop a discrete iterative map formulated as in standard discrete time series models. The Jacobian matrix of the found iterative map is defined and used to compute Lyapunov exponents to prove existence of chaos. Performance of the developed study is positively evaluated by using classical simulations and fine\u2010tuning a bifurcation parameter to detect chaos. This parameter is the desired reference of the inductor current peak. Results show that the proposed scheme is very fast and accurate. The study can be easily extended to other switching topologies of DC\u2010DC inverters.<\/jats:p>","DOI":"10.1155\/2021\/9162259","type":"journal-article","created":{"date-parts":[[2021,8,14]],"date-time":"2021-08-14T19:35:05Z","timestamp":1628969705000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fast Simulation and Chaos Investigation of a DC\u2010DC Boost Inverter"],"prefix":"10.1155","volume":"2021","author":[{"given":"Rachid","family":"Dhifaou","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2162-2461","authenticated-orcid":false,"given":"Houda","family":"Brahmi","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,8,14]]},"reference":[{"key":"e_1_2_12_1_2","unstructured":"De GussemeK. DavidM. Van deS. AlexP. Van denB. andJanA. M. Digital control of boost PFC converters operating in both continuous and discontinuous conduction mode Proceedings of the 35th Annual IEEE Power Electronics Specialists Conference Aachen June 2004 Aachen Germany."},{"key":"e_1_2_12_2_2","unstructured":"JiangW. ZhouY.-f. andChenJ.-n. Modelling and simulation of boost converter in CCM and DCM Proceedings of the 2nd International Conference on Power Electronics and Intelligent Transportation System November 2009 Shenzhen China."},{"key":"e_1_2_12_3_2","doi-asserted-by":"publisher","DOI":"10.3390\/en12010004"},{"key":"e_1_2_12_4_2","unstructured":"ChavesE. N. ViajanteG. P. FreitasM. A. A.et al. Design based on internal model applied in a quadratic boost converter with P&O MPPT Proceedings of the International Conference on Renewable Energies and Power Quality (ICREPQ\u201918) March 2018 Salamanca Spain."},{"key":"e_1_2_12_5_2","doi-asserted-by":"publisher","DOI":"10.3390\/en11082044"},{"key":"e_1_2_12_6_2","doi-asserted-by":"crossref","unstructured":"KaramanakosP. GeyerT. andManiasS. Direct voltage control of DC-DC boost converters using model predictive control based on enumeration Proceedings of the 15th International Power Electronics and Motion Control Conference EPE-PEMC 2012 ECCE Europe September 2012 Novi Sad Serbia.","DOI":"10.1109\/EPEPEMC.2012.6397293"},{"key":"e_1_2_12_7_2","doi-asserted-by":"publisher","DOI":"10.1155\/2017\/4143901"},{"key":"e_1_2_12_8_2","unstructured":"De KeyserR. BonillaJ. andIonescuC. A comparative study of several control techniques applied to a boost converter Proceedings of the IEEE 10th International Conference on Optimisation of Electrical and Electronic Equipment OPTIM December 2006 Brasov Romania."},{"key":"e_1_2_12_9_2","doi-asserted-by":"publisher","DOI":"10.4028\/www.scientific.net\/amm.733.635"},{"key":"e_1_2_12_10_2","first-page":"171","article-title":"Investigation of chaos and bifurcation in boost converter","volume":"18","author":"Jayakumar M.","year":"2018","journal-title":"International Journal of Pure and Applied Mathematics"},{"key":"e_1_2_12_11_2","article-title":"Inductor current sampled feedback control of chaos in current-mode boost converter","volume":"6","author":"Bao B.-C.","year":"2008","journal-title":"Journal of Electronic Science and Technology of China"},{"key":"e_1_2_12_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-7362-2_18"},{"key":"e_1_2_12_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-815838-8.00001-7"},{"key":"e_1_2_12_14_2","doi-asserted-by":"publisher","DOI":"10.1145\/2890500"},{"key":"e_1_2_12_15_2","first-page":"285","article-title":"Determining Lyapunov exponents from a time series","author":"Alan W.","year":"1985","journal-title":"Physica 16D"},{"key":"e_1_2_12_16_2","doi-asserted-by":"crossref","unstructured":"DmitrievaL. A. KuperinY. A. SmetaninN. M. andGermanA.C. Method of calculating Lyapunov exponents for time series using arti\ufb01cial neural networks committees Proceedings of the International Conference Days on Diffraction July 2016 St. Petersburg Russia 127\u2013132.","DOI":"10.1109\/DD.2016.7756827"},{"key":"e_1_2_12_17_2","unstructured":"GuldemirH. Modelling and sliding mode control of Dc-Dc buck-boost converter Proceedings of the 6th International Advanced Technologies Symposium (IATS\u201911) May 2011 Elaz\u0131g Turkey."},{"key":"e_1_2_12_18_2","doi-asserted-by":"publisher","DOI":"10.1080\/13873954.2016.1232283"},{"key":"e_1_2_12_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0064319"},{"key":"e_1_2_12_20_2","doi-asserted-by":"publisher","DOI":"10.1142\/s0218127408020185"},{"key":"e_1_2_12_21_2","doi-asserted-by":"publisher","DOI":"10.1049\/iet-pel.2012.0221"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/9162259.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/9162259.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/9162259","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T21:49:14Z","timestamp":1723240154000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/9162259"}},"subtitle":[],"editor":[{"given":"Guillermo","family":"Huerta Cuellar","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/9162259"],"URL":"https:\/\/doi.org\/10.1155\/2021\/9162259","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2021-05-24","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-07-29","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-08-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"9162259"}}