{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T18:54:30Z","timestamp":1758394470004},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2010,8]]},"abstract":"<jats:p> For a class of cubic nilpotent system, the formulae of the first eight quasi-Lyapunov constants are obtained. We show that the origin of this system is a center if and only if the first eight Lyapunov constants are zeros. Under a small perturbation, eight limit cycles can be created from the eight-order weakened focus. <\/jats:p>","DOI":"10.1142\/s0218127410027210","type":"journal-article","created":{"date-parts":[[2010,11,15]],"date-time":"2010-11-15T09:15:30Z","timestamp":1289812530000},"page":"2579-2584","source":"Crossref","is-referenced-by-count":21,"title":["BIFURCATIONS OF LIMIT CYCLES AND CENTER PROBLEM FOR A CLASS OF CUBIC NILPOTENT SYSTEM"],"prefix":"10.1142","volume":"20","author":[{"given":"YIRONG","family":"LIU","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"JIBIN","family":"LI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China"},{"name":"School of Science, Kunming University of Science and Technology, Kunming, Yunnan 650093, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,5,2]]},"reference":[{"key":"rf1","volume-title":"Nonlinear Oscillations in Second Order Systems","author":"Amelikin B. B.","year":"1982"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405012740"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.05.064"},{"key":"rf4","volume-title":"Stability of Motion, Mathematics in Science and Engineering","volume":"30","author":"Lyapunov A. M.","year":"1966"},{"key":"rf5","first-page":"622","volume":"30","author":"Liu Y.","journal-title":"J. Cent. South Univ. Technol."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409025110"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409024669"},{"key":"rf8","author":"Liu Y. R.","journal-title":"J. Diff. Eqs."},{"key":"rf9","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1017\/S0143385700001553","volume":"2","author":"Moussu R.","journal-title":"Erg. Th. Dyn. Syst."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.2001.4043"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02684366"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127410027210","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:57:19Z","timestamp":1565125039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127410027210"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,8]]},"references-count":11,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2012,5,2]]},"published-print":{"date-parts":[[2010,8]]}},"alternative-id":["10.1142\/S0218127410027210"],"URL":"https:\/\/doi.org\/10.1142\/s0218127410027210","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,8]]}}}