{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T07:04:25Z","timestamp":1774422265413,"version":"3.50.1"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,5]]},"abstract":"<jats:p> Time-periodic perturbations of an asymmetric Duffing\u2013Van-der-Pol equation close to an integrable equation with a homoclinic \"figure-eight\" of a saddle are considered. The behavior of solutions outside the neighborhood of \"figure-eight\" is studied analytically. The problem of limit cycles for an autonomous equation is solved and resonance zones for a nonautonomous equation are analyzed. The behavior of the separatrices of a fixed saddle point of the Poincar\u00e9 map in the small neighborhood of the unperturbed \"figure-eight\" is ascertained. The results obtained are illustrated by numerical computations. <\/jats:p>","DOI":"10.1142\/s0218127414500618","type":"journal-article","created":{"date-parts":[[2014,5,28]],"date-time":"2014-05-28T12:08:41Z","timestamp":1401278921000},"page":"1450061","source":"Crossref","is-referenced-by-count":5,"title":["On Periodic Perturbations of Asymmetric Duffing\u2013Van-der-Pol Equation"],"prefix":"10.1142","volume":"24","author":[{"given":"Albert D.","family":"Morozov","sequence":"first","affiliation":[{"name":"Department of Mechanics and Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Olga S.","family":"Kostromina","sequence":"additional","affiliation":[{"name":"Department of Mechanics and Mathematics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,5,28]]},"reference":[{"key":"rf1","volume-title":"Additional Chapters of the Theory of Ordinary Differential Equations","author":"Arnold V. 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