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For the second class of systems, we prove that there exist [Formula: see text] small-amplitude limit cycles around the origin of the systems for [Formula: see text], and nine limit cycles for [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218127416500267","type":"journal-article","created":{"date-parts":[[2016,3,10]],"date-time":"2016-03-10T03:26:20Z","timestamp":1457580380000},"page":"1650026","source":"Crossref","is-referenced-by-count":2,"title":["Analytic Integrability of Two Lopsided Systems"],"prefix":"10.1142","volume":"26","author":[{"given":"Feng","family":"Li","sequence":"first","affiliation":[{"name":"School of Science, Linyi University, Linyi, Shandong 276005, P. R. 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