{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T18:29:57Z","timestamp":1761762597922},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p> The focus of the paper is mainly on the existence of limit cycles of a planar system with third-degree polynomial functions. A previously developed perturbation technique for computing normal forms of differential equations is employed to calculate the focus values of the system near equilibrium points. Detailed studies have been provided for a number of cases with certain restrictions on system parameters, giving rise to a complete classification for the local dynamical behavior of the system. In particular, a sufficient condition is established for the existence of k small amplitude limit cycles in the neighborhood of a high degenerate critical point. The condition is then used to show that the system can have eight and ten small amplitude (local) limit cycles for a set of particular parameter values. <\/jats:p>","DOI":"10.1142\/s0218127404009247","type":"journal-article","created":{"date-parts":[[2004,3,12]],"date-time":"2004-03-12T08:57:28Z","timestamp":1079081848000},"page":"41-60","source":"Crossref","is-referenced-by-count":28,"title":["A STUDY ON THE EXISTENCE OF LIMIT CYCLES OF A PLANAR SYSTEM WITH THIRD-DEGREE POLYNOMIALS"],"prefix":"10.1142","volume":"14","author":[{"given":"M.","family":"HAN","sequence":"first","affiliation":[{"name":"Department of Mathematics,  Shanghai Jiaotong University, Shanghai 200030, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y.","family":"LIN","sequence":"additional","affiliation":[{"name":"Department of Mathematics,  Shanghai Jiaotong University, Shanghai 200030, P.R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"YU","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, The University  of Western Ontario, London, Ontario, Canada N6A 5B7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"181","volume":"30","author":"Bautin N. N.","journal-title":"Mat. Sbornik (N.S.)"},{"key":"rf2","first-page":"1594","volume":"14","author":"Cherkas L. A.","journal-title":"Diff. 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