{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T15:39:35Z","timestamp":1760888375663},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,4]]},"abstract":"<jats:p> We study the bifurcation of limit cycles in the neighborhood of a 2-polycycle through two hyperbolic saddles with both hyperbolicity ratios being 1. The cyclicity is expressed as an explicit function of saddle quantities. Our results can be applied to the case when both connections are broken under perturbations. <\/jats:p>","DOI":"10.1142\/s0218127409023603","type":"journal-article","created":{"date-parts":[[2009,8,17]],"date-time":"2009-08-17T09:02:26Z","timestamp":1250499746000},"page":"1255-1266","source":"Crossref","is-referenced-by-count":2,"title":["SADDLE QUANTITIES AND CYCLICITY OF 2-POLYCYCLE"],"prefix":"10.1142","volume":"19","author":[{"given":"LIQIN","family":"ZHAO","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"XUEXING","family":"WANG","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"The Theory of Bifurcations of Dynamical Systems on a Plane","author":"Andronov A. A.","year":"1971"},{"key":"rf2","first-page":"181","volume":"30","author":"Bautin N.","journal-title":"Mat. Sbornic (NS)"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1988-031-6"},{"key":"rf4","first-page":"469","volume":"17","author":"Cherkas L. A.","journal-title":"Diferentsial'nye Uravneniya"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511665639"},{"key":"rf6","first-page":"45","volume":"51","author":"Dulac H.","journal-title":"Bull. Soc. Math. France"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/9\/5\/008"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(86)90030-6"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0362-546X(02)00301-2"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2006.11.009"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1070\/RM1991v046n01ABEH002733"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1137\/0148027"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(89)90069-7"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1994.1034"},{"key":"rf15","volume":"28","author":"Leontovich E. A.","journal-title":"Dokl. Akad. Nauk. SSSR."},{"key":"rf16","volume-title":"Normal Form Theory and Application","author":"Li W. G.","year":"2000"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.5802\/afst.786"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/7\/6\/004"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1994.1114"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/BF02584827"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0083072"},{"key":"rf22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4064\/ap-49-1-1-16","volume":"49","author":"Rousseau C.","journal-title":"Ann. Polon. Math."},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.03.028"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1007\/s11425-007-0015-6"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409023603","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:02:20Z","timestamp":1565136140000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409023603"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4]]},"references-count":24,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,4]]}},"alternative-id":["10.1142\/S0218127409023603"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409023603","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4]]}}}