{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:18:34Z","timestamp":1772288314895,"version":"3.50.1"},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2009,12]]},"abstract":"<jats:p> Using algorithms of computational algebra we prove that at most eight limit cycles can bifurcate from any center or focus at the origin of the cubic system [Formula: see text]. That is, an upper bound for cyclicity of the origin of the system is eight. <\/jats:p>","DOI":"10.1142\/s1230161209000323","type":"journal-article","created":{"date-parts":[[2009,11,30]],"date-time":"2009-11-30T04:34:31Z","timestamp":1259555671000},"page":"429-439","source":"Crossref","is-referenced-by-count":10,"title":["The Cyclicity of a Cubic System"],"prefix":"10.1142","volume":"16","author":[{"given":"Viktor","family":"Levandovskyy","sequence":"first","affiliation":[{"name":"Lehrstuhl D f\u00fcr Mathematik, RWTH Aachen University, Templergraben 64, D\u201352062 Aachen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alessandro","family":"Logar","sequence":"additional","affiliation":[{"name":"Department of Matematics, University of Trieste, p. le Europa 1, 34127 Trieste, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Valery G.","family":"Romanovski","sequence":"additional","affiliation":[{"name":"Center for Applied Mathematics and Theoretical Physics, University of Maribor, Krekova 2, SI\u20132000 Maribor, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,1,25]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2005.09.007"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2181-2"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/jfan.1996.3029"},{"key":"rf6","first-page":"146","volume":"6","author":"Gianni P.","journal-title":"J. Symbolic Comput."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.10.057"},{"key":"rf8","series-title":"Nonlinear Analysis: Real World Applications","volume-title":"Integrability conditions for Lotka\u2013Volterra complex quintic systems","author":"Gin\u00e9 J."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-04963-1"},{"key":"rf10","volume-title":"Centre for Computer Algebra","author":"Greuel G.-M.","year":"2005"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.09.051"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-54522-0_108"},{"key":"rf13","series-title":"Graduate Studies in Mathematics","volume-title":"Lectures on analytic differential equations","volume":"86","author":"Ilyashenko Yu.","year":"2008"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/S0747-7171(03)00016-6"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.07.026"},{"key":"rf16","first-page":"1241","volume":"35","author":"Liu Y.-R.","journal-title":"Chinese Sci. Bull."},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403006352"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/34\/47\/326"},{"key":"rf19","first-page":"79","volume":"10","author":"Romanovski V. G.","journal-title":"Nonlinear Phenom. Complex Syst."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1142\/S1230161208000249"},{"key":"rf21","volume-title":"The center and cyclicity problems: a computational algebra approach","author":"Romanovski V. G.","year":"2009"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8798-4"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0052"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1994.1049"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/8\/5\/011"}],"container-title":["Open Systems &amp; Information Dynamics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1230161209000323","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T12:22:26Z","timestamp":1565180546000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1230161209000323"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12]]},"references-count":23,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,1,25]]},"published-print":{"date-parts":[[2009,12]]}},"alternative-id":["10.1142\/S1230161209000323"],"URL":"https:\/\/doi.org\/10.1142\/s1230161209000323","relation":{},"ISSN":["1230-1612","1793-7191"],"issn-type":[{"value":"1230-1612","type":"print"},{"value":"1793-7191","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12]]}}}