{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T19:55:21Z","timestamp":1777492521053,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,8,27]],"date-time":"2020-08-27T00:00:00Z","timestamp":1598486400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we study limit cycle bifurcation near a cuspidal loop for a general near-Hamiltonian system by using expansions of the first order Melnikov functions. We give a method to compute more coefficients of the expansions to find more limit cycles near the cuspidal loop. As an application example, we considered a polynomial near-Hamiltonian system and found 12 limit cycles near the cuspidal loop and the center.<\/jats:p>","DOI":"10.3390\/sym12091425","type":"journal-article","created":{"date-parts":[[2020,8,27]],"date-time":"2020-08-27T09:47:02Z","timestamp":1598521622000},"page":"1425","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Limit Cycle Bifurcations Near a Cuspidal Loop"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5121-6096","authenticated-orcid":false,"given":"Pan","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maoan","family":"Han","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China"},{"name":"Department of Mathematics, Shanghai Normal University, Shanghai 200234, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1250296","DOI":"10.1142\/S0218127412502963","article-title":"Asymptotic expansions of Melnikov functions and limit cycle bifurcations","volume":"22","author":"Han","year":"2012","journal-title":"Int. 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