{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T06:07:28Z","timestamp":1774591648116,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,8]]},"abstract":"<jats:p> We consider van der Pol\u2013Duffing oscillators coupled via a two-dimensional linear system, representing Huygens coupling. We demonstrate that two identical synchronized oscillators can have chaotic movements and exhibit Shilnikov chaos. We rigorously prove the existence of a homoclinic orbit of a saddle-focus and a symmetrical heteroclinic contour of two saddle-foci, leading to the appearance of chaos via the Shilnikov saddle-focus bifurcation. We also support our analytical results with numerical simulations, revealing the main signature of Shilnikov chaos, the coexistence of chaotic and regular attractors with riddled basins of attraction, including wild attractors. <\/jats:p>","DOI":"10.1142\/s0218127414400070","type":"journal-article","created":{"date-parts":[[2014,8,29]],"date-time":"2014-08-29T04:35:53Z","timestamp":1409286953000},"page":"1440007","source":"Crossref","is-referenced-by-count":9,"title":["Shilnikov Chaos in Oscillators with Huygens Coupling"],"prefix":"10.1142","volume":"24","author":[{"given":"Vladimir N.","family":"Belykh","sequence":"first","affiliation":[{"name":"Department of Mathematics, Volga State Academy, 5A, Nesterov Str., Nizhny Novgorod, 603950, Russia"},{"name":"Department of Control Theory, Lobachevsky State University of Nizhny Novgorod, 23, Gagarin Ave., Nizhny Novgorod, 603950, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Evgeniya V.","family":"Pankratova","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Volga State Academy, 5A, Nesterov Str., Nizhny Novgorod, 603950, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,8,29]]},"reference":[{"key":"rf2","unstructured":"V. N.\u00a0Belykh, Advances in the Mathematical Sciences, American Mathematical Society Translations\u00a0200 (2000)\u00a0pp. 51\u201362."},{"key":"rf4","first-page":"595","volume":"9","author":"Belyustina L. N.","year":"1973","journal-title":"Diff. Uravneniya"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2001.0888"},{"key":"rf6","volume-title":"Synchronization in Science and Technology","author":"Blekhman I. I.","year":"1988"},{"key":"rf7","unstructured":"W. T.\u00a0Oud, H.\u00a0Nijmeijer and A. Yu.\u00a0Pogromsky, Group Coordinations and Control, eds. K. Y.\u00a0Pettersen, J. T.\u00a0Gravdahl and H.\u00a0Nijmeijer (Springer, Berlin, 2006)\u00a0pp. 66\u201376."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1119\/1.1501118"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127492000525"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127496000527"},{"key":"rf12","first-page":"163","volume":"6","author":"Shilnikov L. P.","year":"1965","journal-title":"Sov. Math. Dokl."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/9789812798596"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/9789812798558"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.4249\/scholarpedia.1891"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127414400070","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:32:15Z","timestamp":1565109135000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414400070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,8]]},"references-count":12,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2014,8,29]]},"published-print":{"date-parts":[[2014,8]]}},"alternative-id":["10.1142\/S0218127414400070"],"URL":"https:\/\/doi.org\/10.1142\/s0218127414400070","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,8]]}}}