{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:42:36Z","timestamp":1740120156217,"version":"3.37.3"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11572224"],"award-info":[{"award-number":["11572224"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11772229"],"award-info":[{"award-number":["11772229"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2018,2]]},"abstract":"<jats:p> Time delay is inevitable in unidirectionally coupled drive-free vibratory gyroscope system. The effect of time delay on the gyroscope system is studied in this paper. To this end, amplitude death and Hopf bifurcation induced by small time delay are first investigated by analyzing the related characteristic equation. Then, the direction of Hopf bifurcations and stability of Hopf-bifurcating periodic oscillations are determined by calculating the normal form on the center manifold. Next, spatiotemporal patterns of these Hopf-bifurcating periodic oscillations are analyzed by using the symmetric bifurcation theory of delay differential equations. Finally, it is found that numerical simulations agree with the associated analytic results. These phenomena could be induced although time delay is very small. Therefore, it is shown that time delay is an important factor which influences the sensitivity and accuracy of the gyroscope system and cannot be neglected during the design and manufacture. <\/jats:p>","DOI":"10.1142\/s0218127418500293","type":"journal-article","created":{"date-parts":[[2018,3,22]],"date-time":"2018-03-22T05:16:50Z","timestamp":1521695810000},"page":"1850029","source":"Crossref","is-referenced-by-count":2,"title":["Bifurcation Analysis and Spatiotemporal Patterns in Unidirectionally Delay-Coupled Vibratory Gyroscopes"],"prefix":"10.1142","volume":"28","author":[{"given":"Li","family":"Li","sequence":"first","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3521-6843","authenticated-orcid":false,"given":"Jian","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,3,22]]},"reference":[{"volume-title":"MEMS Vibratory Gyroscopes: Structural Approaches to Improve Robustness","year":"2008","author":"Acar C.","key":"S0218127418500293BIB001"},{"key":"S0218127418500293BIB002","doi-asserted-by":"publisher","DOI":"10.1166\/sl.2004.057"},{"key":"S0218127418500293BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8159-4"},{"key":"S0218127418500293BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/JSEN.2016.2640290"},{"key":"S0218127418500293BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/1050-6411(92)90017-D"},{"key":"S0218127418500293BIB006","doi-asserted-by":"publisher","DOI":"10.1145\/513001.513002"},{"key":"S0218127418500293BIB007","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718195"},{"key":"S0218127418500293BIB008","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.74.1570"},{"key":"S0218127418500293BIB009","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1995.1145"},{"key":"S0218127418500293BIB010","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1995.1144"},{"key":"S0218127418500293BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/S0005-1098(01)00265-5"},{"key":"S0218127418500293BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4574-2"},{"key":"S0218127418500293BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4342-7"},{"volume-title":"Theory and Applications of Hopf Bifurcation","year":"1981","author":"Hassard B. D.","key":"S0218127418500293BIB015"},{"key":"S0218127418500293BIB016","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.795"},{"key":"S0218127418500293BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-05030-9"},{"key":"S0218127418500293BIB018","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.2009.0243"},{"key":"S0218127418500293BIB019","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.79.2911"},{"key":"S0218127418500293BIB020","doi-asserted-by":"publisher","DOI":"10.1109\/TIE.2016.2569462"},{"key":"S0218127418500293BIB021","volume-title":"Handbook of Chaos Control","author":"Sch\u00f6ll E.","year":"2008","edition":"2"},{"key":"S0218127418500293BIB022","doi-asserted-by":"publisher","DOI":"10.1063\/1.3578046"},{"key":"S0218127418500293BIB023","doi-asserted-by":"publisher","DOI":"10.1109\/TNNLS.2012.2209459"},{"key":"S0218127418500293BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-2619-2"},{"key":"S0218127418500293BIB025","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.031108"},{"key":"S0218127418500293BIB026","doi-asserted-by":"publisher","DOI":"10.1063\/1.3532802"},{"key":"S0218127418500293BIB027","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-98-02083-2"},{"key":"S0218127418500293BIB028","doi-asserted-by":"publisher","DOI":"10.1137\/040614207"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127418500293","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,21]],"date-time":"2019-09-21T20:39:05Z","timestamp":1569098345000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127418500293"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,2]]},"references-count":27,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2018,3,22]]},"published-print":{"date-parts":[[2018,2]]}},"alternative-id":["10.1142\/S0218127418500293"],"URL":"https:\/\/doi.org\/10.1142\/s0218127418500293","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2018,2]]}}}