{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,20]],"date-time":"2025-09-20T21:13:48Z","timestamp":1758402828242,"version":"3.37.3"},"reference-count":23,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Guangxi Education Department","award":["ZD2014131","HZUBS201302","11261013","11371373"],"award-info":[{"award-number":["ZD2014131","HZUBS201302","11261013","11371373"]}]},{"name":"Research Foundation of Hezhou University","award":["ZD2014131","HZUBS201302","11261013","11371373"],"award-info":[{"award-number":["ZD2014131","HZUBS201302","11261013","11371373"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZD2014131","HZUBS201302","11261013","11371373"],"award-info":[{"award-number":["ZD2014131","HZUBS201302","11261013","11371373"]}],"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":["ZD2014131","HZUBS201302","11261013","11371373"],"award-info":[{"award-number":["ZD2014131","HZUBS201302","11261013","11371373"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>We investigate multiple limit cycles bifurcation and center-focus problem of the degenerate equilibrium for a three-dimensional system. By applying the method of symbolic computation, we obtain the first four quasi-Lyapunov constants. It is proved that the system can generate 3 small limit cycles from nilpotent critical point on center manifold. Furthermore, the center conditions are found and as weak foci the highest order is proved to be the fourth; thus we obtain at most 3 small limit cycles from the origin via local bifurcation. To our knowledge, it is the first example of multiple limit cycles bifurcating from a nilpotent singularity for the flow of a high-dimensional system restricted to the center manifold.<\/jats:p>","DOI":"10.1155\/2014\/546243","type":"journal-article","created":{"date-parts":[[2014,7,9]],"date-time":"2014-07-09T21:04:50Z","timestamp":1404939890000},"page":"1-8","source":"Crossref","is-referenced-by-count":2,"title":["The Center Conditions and Bifurcation of Limit Cycles at the Degenerate Singularity of a Three-Dimensional System"],"prefix":"10.1155","volume":"2014","author":[{"given":"Shugang","family":"Song","sequence":"first","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingjing","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Information and Mathematics, Yangtze University, Jingzhou 434023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qinlong","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Hezhou University, Hezhou 542899, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1982","key":"1"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/S0960-0779(03)00334-5"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2009.01.049"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023159"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0893-9659(94)90095-7"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(02)00129-3"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.03.111"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.03.113"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.bulsci.2009.12.001"},{"volume":"35","year":"1981","series-title":"Applied Mathematical Sciences","key":"10"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2005.05.064"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405012740"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1017\/S014338570200127X"},{"issue":"2","key":"14","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1017\/S0143385700001553","volume":"2","year":"1982","journal-title":"Ergodic Theory and Dynamical Systems"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1023\/A:1025192613518"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2006.03.012"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410027210"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411029161"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2010.06.017"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2012.03.009"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2011.11.006"},{"volume":"2010","journal-title":"Electronic Journal of Differential Equations","year":"2010","key":"22"},{"issue":"1","key":"23","doi-asserted-by":"crossref","first-page":"33","DOI":"10.11948\/2011004","volume":"1","year":"2011","journal-title":"The Journal of Applied Analysis and Computation"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/546243.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/546243.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/546243.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,4,10]],"date-time":"2022-04-10T18:47:34Z","timestamp":1649616454000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/546243\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":23,"alternative-id":["546243","546243"],"URL":"https:\/\/doi.org\/10.1155\/2014\/546243","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}