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Bifurcation Chaos"],"published-print":{"date-parts":[[2017,11]]},"abstract":"<jats:p> A popular biomathematics model of the Goodwin oscillator has been previously generalized to a more biologically plausible construct by introducing three time delays to portray the transport phenomena arising due to the spatial distribution of the model states. The present paper addresses a similar conversion of an impulsive version of the Goodwin oscillator that has found application in mathematical modeling, e.g. in endocrine systems with pulsatile hormone secretion. While the cascade structure of the linear continuous part pertinent to the Goodwin oscillator is preserved in the impulsive Goodwin oscillator, the static nonlinear feedback of the former is substituted with a pulse modulation mechanism thus resulting in hybrid dynamics of the closed-loop system. To facilitate the analysis of the mathematical model under investigation, a discrete mapping propagating the continuous state variables through the firing times of the impulsive feedback is derived. Due to the presence of multiple time delays in the considered model, previously developed mapping derivation approaches are not applicable here and a novel technique is proposed and applied. The mapping captures the dynamics of the original hybrid system and is instrumental in studying complex nonlinear phenomena arising in the impulsive Goodwin oscillator. A simulation example is presented to demonstrate the utility of the proposed approach in bifurcation analysis. <\/jats:p>","DOI":"10.1142\/s0218127417501826","type":"journal-article","created":{"date-parts":[[2017,12,18]],"date-time":"2017-12-18T03:20:32Z","timestamp":1513567232000},"page":"1750182","source":"Crossref","is-referenced-by-count":5,"title":["Discrete-Time Mapping for an Impulsive Goodwin Oscillator with Three Delays"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8839-3977","authenticated-orcid":false,"given":"Alexander N.","family":"Churilov","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Mechanics, St. Petersburg State University, Universitetsky av. 28, Stary Peterhof, 198504, St. Petersburg, Russia"},{"name":"Laboratory of Control of Multi-Agent, Distributed and Networked Systems, ITMO University, Kronverkskiy Pr. 49, 197101, St. Petersburg, Russia"}]},{"given":"Alexander","family":"Medvedev","sequence":"additional","affiliation":[{"name":"Department of Information Technology, Uppsala University, L\u00e4gerhyddsv\u00e4gen 2, SE-751 05, Uppsala, Sweden"}]},{"given":"Zhanybai T.","family":"Zhusubaliyev","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Southwest State University, 50 Years of October Str. 94, 305040, Kursk, Russia"}]}],"member":"219","published-online":{"date-parts":[[2017,12,18]]},"reference":[{"volume-title":"Impulsive Differential Equations: Periodic Solutions and Applications","year":"1993","author":"Bainov D.","key":"S0218127417501826BIB001"},{"key":"S0218127417501826BIB002","doi-asserted-by":"publisher","DOI":"10.1111\/j.1365-2265.2007.02976.x"},{"key":"S0218127417501826BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2011.05.010"},{"key":"S0218127417501826BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-5193(86)80158-8"},{"key":"S0218127417501826BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2008.06.016"},{"key":"S0218127417501826BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2014.05.021"},{"key":"S0218127417501826BIB008","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2013.2273284"},{"key":"S0218127417501826BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/s00498-016-0160-y"},{"key":"S0218127417501826BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2015.08.004"},{"key":"S0218127417501826BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/0303-2647(94)90019-1"},{"key":"S0218127417501826BIB012","doi-asserted-by":"publisher","DOI":"10.1186\/1753-4631-4-5"},{"key":"S0218127417501826BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2016.05.002"},{"key":"S0218127417501826BIB014","doi-asserted-by":"publisher","DOI":"10.1155\/2007\/72561"},{"key":"S0218127417501826BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/s00285-004-0291-5"},{"key":"S0218127417501826BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/S0076-6879(08)03814-7"},{"key":"S0218127417501826BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1760-2"},{"key":"S0218127417501826BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/0065-2571(65)90067-1"},{"key":"S0218127417501826BIB019","doi-asserted-by":"publisher","DOI":"10.1038\/209479a0"},{"key":"S0218127417501826BIB020","doi-asserted-by":"publisher","DOI":"10.1515\/9781400865246"},{"key":"S0218127417501826BIB021","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1831-1"},{"key":"S0218127417501826BIB022","doi-asserted-by":"publisher","DOI":"10.1142\/0906"},{"key":"S0218127417501826BIB023","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413300024"},{"key":"S0218127417501826BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(01)00260-7"},{"key":"S0218127417501826BIB025","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1979.1102124"},{"key":"S0218127417501826BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-10984-8_2"},{"key":"S0218127417501826BIB028","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(97)00019-8"},{"key":"S0218127417501826BIB029","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171204307271"},{"key":"S0218127417501826BIB030","doi-asserted-by":"crossref","DOI":"10.1007\/b98868","volume-title":"Mathematical Biology, I: An Introduction","author":"Murray J. 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