{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T06:43:43Z","timestamp":1740120223872,"version":"3.37.3"},"reference-count":16,"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":["11271261)"],"award-info":[{"award-number":["11271261)"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,6,15]]},"abstract":"<jats:p> This paper is concerned with the bifurcation problem of limit cycles by perturbing a piecewise Hamiltonian system with a double homoclinic loop. First, the derivative of the first Melnikov function is provided. Then, we use it, together with the analytic method, to derive the asymptotic expansion of the first Melnikov function near the loop. Meanwhile, we present the first coefficients in the expansion, which can be applied to study the limit cycle bifurcation near the loop. We give sufficient conditions for this system to have [Formula: see text] limit cycles in the neighborhood of the loop. As an application, a piecewise polynomial Li\u00e9nard system is investigated, finding six limit cycles with the help of the obtained method. <\/jats:p>","DOI":"10.1142\/s0218127416501030","type":"journal-article","created":{"date-parts":[[2016,6,29]],"date-time":"2016-06-29T02:02:54Z","timestamp":1467165774000},"page":"1650103","source":"Crossref","is-referenced-by-count":7,"title":["Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop"],"prefix":"10.1142","volume":"26","author":[{"given":"Yanqin","family":"Xiong","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,6,28]]},"reference":[{"key":"S0218127416501030BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-008-9108-3"},{"key":"S0218127416501030BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409025250"},{"key":"S0218127416501030BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2008.06.039"},{"key":"S0218127416501030BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.asr.2008.08.025"},{"key":"S0218127416501030BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127412501891"},{"volume-title":"Bifurcation Theory of Limit Cycles","year":"2013","author":"Han M.","key":"S0218127416501030BIB006"},{"key":"S0218127416501030BIB007","first-page":"809","volume":"5","author":"Han M.","year":"2015","journal-title":"J. Appl. Anal. Comput."},{"key":"S0218127416501030BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2011.09.013"},{"key":"S0218127416501030BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2012.03.022"},{"key":"S0218127416501030BIB010","doi-asserted-by":"publisher","DOI":"10.1142\/S021812741002654X"},{"key":"S0218127416501030BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.09.125"},{"key":"S0218127416501030BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.05.041"},{"key":"S0218127416501030BIB013","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/575390"},{"key":"S0218127416501030BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2014.05.035"},{"key":"S0218127416501030BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.12.035"},{"key":"S0218127416501030BIB016","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2012.03.052"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127416501030","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,1]],"date-time":"2019-10-01T18:29:34Z","timestamp":1569954574000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127416501030"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,15]]},"references-count":16,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2016,6,28]]},"published-print":{"date-parts":[[2016,6,15]]}},"alternative-id":["10.1142\/S0218127416501030"],"URL":"https:\/\/doi.org\/10.1142\/s0218127416501030","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"type":"print","value":"0218-1274"},{"type":"electronic","value":"1793-6551"}],"subject":[],"published":{"date-parts":[[2016,6,15]]}}}