{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T16:14:24Z","timestamp":1760890464255,"version":"3.41.2"},"reference-count":25,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971145"],"award-info":[{"award-number":["11971145"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["A2019205133"],"award-info":[{"award-number":["A2019205133"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2022,5]]},"abstract":"<jats:p> In this paper, we study the expansion of the first order Melnikov function near a heteroclinic loop with two nilpotent cusps of general order. More precisely, the order of the two cusps is [Formula: see text] and [Formula: see text] respectively, where [Formula: see text] [Formula: see text]. For general [Formula: see text] and [Formula: see text], we give the expansion of the first order Melnikov function and the formulas for the first few coefficients. We further give a general theorem on the number of limit cycles bifurcated from the heteroclinic loop. These results extend the existing results for [Formula: see text], [Formula: see text] and [Formula: see text] [Formula: see text]. As an application, these results are applied to study the number of limit cycles near a heteroclinic loop with two cusps of different order. <\/jats:p>","DOI":"10.1142\/s0218127422500833","type":"journal-article","created":{"date-parts":[[2022,5,27]],"date-time":"2022-05-27T11:36:12Z","timestamp":1653651372000},"source":"Crossref","is-referenced-by-count":2,"title":["Limit Cycle Bifurcations Near a Heteroclinic Loop with Two Nilpotent Cusps of General Order"],"prefix":"10.1142","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1627-0035","authenticated-orcid":false,"given":"Junmin","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei 050024, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xing","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Hebei Normal University, Shijiazhuang, Hebei 050024, P. R. 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