{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T09:53:51Z","timestamp":1649066031627},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:p> We study a polynomial Li\u00e9nard system depending on three parameters a, b, c and exhibiting the following properties: (i) The origin is the unique equilibrium for all parameters. (ii) If a crosses zero, then the origin changes its stability, and Andronov\u2013Hopf bifurcation arises. We consider a as control parameter and investigate the dependence of Andronov\u2013Hopf bifurcation on the \"unfolding\" parameters b and c. We establish and describe analytically the existence of surfaces and curves located near the origin in the parameter space connected with the existence of small-amplitude limit cycles of multiplicity two and three (existence of degenerate Andronov\u2013Hopf bifurcation). <\/jats:p>","DOI":"10.1142\/s0218127412502719","type":"journal-article","created":{"date-parts":[[2012,12,13]],"date-time":"2012-12-13T04:14:17Z","timestamp":1355372057000},"page":"1250271","source":"Crossref","is-referenced-by-count":1,"title":["ANDRONOV\u2013HOPF BIFURCATION OF HIGHER CODIMENSIONS IN A LI\u00c9NARD SYSTEM"],"prefix":"10.1142","volume":"22","author":[{"given":"ALEXANDER","family":"GRIN","sequence":"first","affiliation":[{"name":"Grodno State University, Ozheshko Street 22, 230023 Grodno, Belarus"}]},{"given":"KLAUS R.","family":"SCHNEIDER","sequence":"additional","affiliation":[{"name":"Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany"}]}],"member":"219","published-online":{"date-parts":[[2012,12,13]]},"reference":[{"key":"rf1","volume-title":"Theory of Bifurcations of Dynamic Systems on a Plane","author":"Andronov A. A.","year":"1973"},{"key":"rf2","volume-title":"Behavior of Dynamical Systems near the Boundaries of Stability Regions","author":"Bautin N. N.","year":"1949"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100061636"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1988-031-6"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2012.08.011"},{"key":"rf6","first-page":"1099","volume":"9","author":"Cherkas L. A.","journal-title":"Diff. Eqs."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(81)90045-0"},{"key":"rf8","volume-title":"Functional Analysis","author":"Kantorovich L. P.","year":"1984"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2421-9"},{"key":"rf10","first-page":"289","volume":"5","author":"Leonov G. A.","journal-title":"Diff. Eq. Dyn. Syst."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1134\/S102833580905005X"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/s10958-009-9388-0"},{"key":"rf13","series-title":"Applied Mathematical Sciences","volume-title":"Averaging Methods in Nonlinear Dynamical Systems","volume":"59","author":"Sanders J. A.","year":"2007"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-2122-6"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(73)90062-4"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127412502719","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T14:50:07Z","timestamp":1565103007000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127412502719"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,11]]},"references-count":15,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2012,12,13]]},"published-print":{"date-parts":[[2012,11]]}},"alternative-id":["10.1142\/S0218127412502719"],"URL":"https:\/\/doi.org\/10.1142\/s0218127412502719","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,11]]}}}