{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T17:11:50Z","timestamp":1765041110966},"reference-count":30,"publisher":"World Scientific Pub Co Pte Lt","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2020,11]]},"abstract":"<jats:p> This paper addresses the issues on the dynamics of nonlinear damping gyros subjected to a quintic nonlinear parametric excitation. The fixed points and their stability are analyzed for the autonomous gyros equation. The number of fixed points of the system varies from one to six. The approximate equation of gyros is considered by expanding the nonlinear restoring force and parametric excitation for the study of the dynamics of gyros. Amplitude and frequency of possible resonances are found by using the multiple scales method. Also obtained are the principal parametric resonance and orders 4 and 6 subharmonic resonances. The stability conditions for each of these resonances are also obtained. Chaotic oscillations, multistability, hysteresis, and coexisting attractors are found using the bifurcation diagrams, the Lyapunov exponents, the phase portraits, the Poincar\u00e9 section and the time histories. The effects of the damping parameter, the angular spin velocity and the parametric nonlinear excitation are analyzed. Results obtained by using the approximate gyros equation are compared to the dynamics obtained with the exact equation of gyros. The analytical investigations are complemented by numerical simulations. <\/jats:p>","DOI":"10.1142\/s021812742050203x","type":"journal-article","created":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T09:18:45Z","timestamp":1606468725000},"page":"2050203","source":"Crossref","is-referenced-by-count":11,"title":["Nonlinear Oscillations of Nonlinear Damping Gyros: Resonances, Hysteresis and Multistability"],"prefix":"10.1142","volume":"30","author":[{"given":"C. H.","family":"Miwadinou","sequence":"first","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire, et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB);, Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, B\u00e9nin"},{"name":"D\u00e9partement de Physique, ENS-Natitingou, (UNSTIM)-Abomey, B\u00e9nin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. V.","family":"Monwanou","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire, et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB);, Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, B\u00e9nin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"L. A.","family":"Hinvi","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire, et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB);, Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, B\u00e9nin"},{"name":"Department of Industrial Computer and Electrical Engineering, University of Abomey, UIT-Lokossa, B\u00e9nin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V. Kamdoum","family":"Tamba","sequence":"additional","affiliation":[{"name":"Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, P. O. Box: 134, Bandjoun, Cameroon"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. A.","family":"Koukp\u00e9m\u00e8dji","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire, et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB);, Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, B\u00e9nin"},{"name":"D\u00e9partement de Physique, FAST-Natitingou, (UNSTIM)-Abomey, B\u00e9nin"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. B.","family":"Chabi Orou","sequence":"additional","affiliation":[{"name":"Laboratoire de M\u00e9canique des Fluides, de la Dynamique Nonlin\u00e9aire, et de la Mod\u00e9lisation des Syst\u00e8mes Biologiques (LMFDNMSB);, Institut de Math\u00e9matiques et de Sciences Physiques, Porto-Novo, B\u00e9nin"},{"name":"D\u00e9partement de Physique, FAST-Natitingou, (UNSTIM)-Abomey, B\u00e9nin"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2020,11,25]]},"reference":[{"key":"S021812742050203XBIB001","doi-asserted-by":"crossref","first-page":"110505","DOI":"10.1088\/1674-1056\/21\/11\/110505","volume":"21","author":"Aghababa M. P.","year":"2012","journal-title":"Chin. Phys. B"},{"key":"S021812742050203XBIB002","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/s11071-008-9347-1","volume":"54","author":"Asokanthan S. F.","year":"2008","journal-title":"Nonlin. Dyn."},{"key":"S021812742050203XBIB003","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1006\/jsvi.2001.4186","volume":"255","author":"Chen H.-K.","year":"2002","journal-title":"J. Sound Vibr."},{"key":"S021812742050203XBIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411029513"},{"key":"S021812742050203XBIB005","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1016\/S0022-460X(03)00343-2","volume":"268","author":"Dooren R. V.","year":"2003","journal-title":"J. Sound Vibr."},{"key":"S021812742050203XBIB006","doi-asserted-by":"crossref","first-page":"032308","DOI":"10.1063\/1.2841032","volume":"15","author":"Enjieu Kadji H. G.","year":"2008","journal-title":"Phys. Plasmas"},{"key":"S021812742050203XBIB007","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1134\/S2075108714030043","volume":"5","author":"Evstifeev M. I.","year":"2014","journal-title":"Gyroscopy and Navigation"},{"key":"S021812742050203XBIB008","doi-asserted-by":"crossref","first-page":"050401","DOI":"10.1088\/1674-1056\/21\/5\/050401","volume":"21","author":"Fan S.-C.","year":"2012","journal-title":"Chin. Phys. B"},{"key":"S021812742050203XBIB009","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1006\/jsvi.1996.0348","volume":"194","author":"Ge Z.-M.","year":"1996","journal-title":"J. Sound Vibr."},{"key":"S021812742050203XBIB010","doi-asserted-by":"crossref","first-page":"1954","DOI":"10.1143\/JJAP.35.1954","volume":"35","author":"Ge Z.-M.","year":"1996","journal-title":"Jpn. J. Appl. Phys."},{"key":"S021812742050203XBIB011","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1006\/jsvi.1996.0561","volume":"198","author":"Ge Z.-M.","year":"1996","journal-title":"J. Sound Vibr."},{"key":"S021812742050203XBIB012","volume-title":"Nonlinear Oscillations in Physical Systems","author":"Hayashi C.","year":"1964"},{"key":"S021812742050203XBIB013","doi-asserted-by":"crossref","first-page":"529","DOI":"10.5194\/ms-10-529-2019","volume":"10","author":"Iskakov Z.","year":"2019","journal-title":"Mech. Sci."},{"key":"S021812742050203XBIB014","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1007\/s12043-018-1586-1","volume":"91","author":"Kamdoum Tamba V.","year":"2018","journal-title":"Pramana \u2014 J. Phys."},{"key":"S021812742050203XBIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127418300318"},{"key":"S021812742050203XBIB016","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/j.physleta.2005.06.020","volume":"343","author":"Lei Y.","year":"2005","journal-title":"Phys. Lett. A"},{"key":"S021812742050203XBIB017","volume":"9","author":"Liu H.","year":"2013","journal-title":"iJOE"},{"key":"S021812742050203XBIB018","first-page":"850612","volume":"2015","author":"Loembe-Souamy R. M. D.","year":"2015","journal-title":"Math. Prob. Eng."},{"key":"S021812742050203XBIB019","doi-asserted-by":"crossref","first-page":"100503","DOI":"10.1088\/1674-1056\/20\/10\/100503","volume":"20","author":"Min F.-H.","year":"2011","journal-title":"Chin. Phys. B"},{"key":"S021812742050203XBIB020","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127416500851"},{"key":"S021812742050203XBIB021","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1007\/s11071-016-3232-0","volume":"88","author":"Miwadinou C. H.","year":"2017","journal-title":"Nonlin. Dyn."},{"key":"S021812742050203XBIB022","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1007\/s12043-019-1839-7","volume":"93","author":"Miwadinou C. H.","year":"2019","journal-title":"Pramana \u2014 J. Phys."},{"key":"S021812742050203XBIB023","volume-title":"Introduction to Perturbation Techniques","author":"Nayfeh A. H.","year":"1981"},{"key":"S021812742050203XBIB024","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1007\/s11071-006-9078-0","volume":"48","author":"Polo M. F. P.","year":"2007","journal-title":"Nonlin. Dyn."},{"key":"S021812742050203XBIB025","doi-asserted-by":"crossref","first-page":"2536","DOI":"10.1016\/j.cnsns.2009.09.022","volume":"15","author":"Roopaei M.","year":"2010","journal-title":"Commun. Nonlin. Sci. Numer. Simulat."},{"key":"S021812742050203XBIB026","doi-asserted-by":"crossref","first-page":"760","DOI":"10.1016\/j.jsv.2007.11.058","volume":"33","author":"Salariech H.","year":"2008","journal-title":"J. Sound Vibr."},{"key":"S021812742050203XBIB027","first-page":"365","volume-title":"23rd Aachen Colloquium Automobile and Engine Technology","author":"Scheurich B.","year":"2014"},{"key":"S021812742050203XBIB028","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/j.chaos.2003.12.014","volume":"21","author":"Siewe Siewe M.","year":"2004","journal-title":"Chaos Solit. Fract."},{"key":"S021812742050203XBIB029","first-page":"462","volume":"9","author":"Vaidyanathan S.","year":"2016","journal-title":"Int. J. Chem. Tech. Res."},{"key":"S021812742050203XBIB030","doi-asserted-by":"crossref","first-page":"2381","DOI":"10.4028\/www.scientific.net\/AMR.139-141.2381","volume":"139","author":"Wang R.","year":"2010","journal-title":"Adv. Mater. Res."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812742050203X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,27]],"date-time":"2020-11-27T09:19:31Z","timestamp":1606468771000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812742050203X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11]]},"references-count":30,"journal-issue":{"issue":"14","published-print":{"date-parts":[[2020,11]]}},"alternative-id":["10.1142\/S021812742050203X"],"URL":"https:\/\/doi.org\/10.1142\/s021812742050203x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11]]}}}