{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,24]],"date-time":"2024-01-24T00:59:31Z","timestamp":1706057971494},"reference-count":49,"publisher":"World Scientific Pub Co Pte Lt","issue":"14","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2017,12,30]]},"abstract":" Starting from historical researches, we used, like Van der Pol and Le Corbeiller, a cubic function for modeling the current\u2013voltage characteristic of a direct current low-pressure plasma discharge tube, i.e. a neon tube. This led us to propose a new four-dimensional autonomous dynamical system allowing to describe the experimentally observed phenomenon. Then, mathematical analysis and detailed numerical investigations of such a fourth-order torus circuit enabled to highlight bifurcation routes from torus breakdown to homoclinic chaos following the Newhouse\u2013Ruelle\u2013Takens scenario. <\/jats:p>","DOI":"10.1142\/s0218127417502200","type":"journal-article","created":{"date-parts":[[2018,1,29]],"date-time":"2018-01-29T03:58:05Z","timestamp":1517198285000},"page":"1750220","source":"Crossref","is-referenced-by-count":5,"title":["Torus Breakdown and Homoclinic Chaos in a Glow Discharge Tube"],"prefix":"10.1142","volume":"27","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-1400-4136","authenticated-orcid":false,"given":"Jean-Marc","family":"Ginoux","sequence":"first","affiliation":[{"name":"Laboratoire des Sciences de l\u2019Information et des Syst\u00e8mes, UMR CNRS 7296, CS 60584, 83041 Toulon Cedex 9, France"}]},{"given":"Riccardo","family":"Meucci","sequence":"additional","affiliation":[{"name":"Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, 50125 Firenze, Italy"}]},{"given":"Stefano","family":"Euzzor","sequence":"additional","affiliation":[{"name":"Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo E. Fermi 6, 50125 Firenze, Italy"}]}],"member":"219","published-online":{"date-parts":[[2018,1,28]]},"reference":[{"key":"S0218127417502200BIB002","first-page":"3","volume":"6","author":"Andronov A.","year":"1939","journal-title":"Uchen. Zap. Gork. Univ."},{"key":"S0218127417502200BIB003","volume-title":"Theory of Bifurcations of Dynamical Systems on a Plane","author":"Andronov A.","year":"1971"},{"key":"S0218127417502200BIB004","doi-asserted-by":"crossref","volume-title":"Dynamical Systems V. Encyclopaedia of Mathematical Sciences","author":"Arnold V.","year":"1994","DOI":"10.1007\/978-3-642-57884-7"},{"key":"S0218127417502200BIB005","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.58.4413"},{"key":"S0218127417502200BIB006","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971484"},{"key":"S0218127417502200BIB007","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.68.2770"},{"key":"S0218127417502200BIB008","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-20.3.180"},{"key":"S0218127417502200BIB009","doi-asserted-by":"publisher","DOI":"10.2307\/1969181"},{"key":"S0218127417502200BIB010","doi-asserted-by":"publisher","DOI":"10.2307\/1969411"},{"key":"S0218127417502200BIB011","doi-asserted-by":"publisher","DOI":"10.2307\/1969465"},{"key":"S0218127417502200BIB012","first-page":"577","volume":"287","author":"Coullet P.","year":"1978","journal-title":"Comptes Rendus de l\u2019Acad\u00e9mie des Sciences de Paris"},{"key":"S0218127417502200BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0101779"},{"key":"S0218127417502200BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127407019287"},{"key":"S0218127417502200BIB015","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.57.617"},{"key":"S0218127417502200BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/BF01020332"},{"key":"S0218127417502200BIB017","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.1972.21.21017"},{"key":"S0218127417502200BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(93)90284-8"},{"key":"S0218127417502200BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/BF01656003"},{"key":"S0218127417502200BIB020","doi-asserted-by":"publisher","DOI":"10.1063\/1.4867672"},{"key":"S0218127417502200BIB021","doi-asserted-by":"publisher","DOI":"10.1063\/1.4919962"},{"key":"S0218127417502200BIB022","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127410027866"},{"key":"S0218127417502200BIB023","doi-asserted-by":"publisher","DOI":"10.1007\/s00407-012-0101-1"},{"key":"S0218127417502200BIB024","doi-asserted-by":"publisher","DOI":"10.1142\/9789814434805_0040"},{"key":"S0218127417502200BIB025","unstructured":"Ginoux, J. M. [2015] Histoire de la Th\u00e9orie des Oscillations non Lin\u00e9aires en France (1880\u20131940) (Hermann, Paris), pp. 558."},{"key":"S0218127417502200BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-29701-9_2"},{"key":"S0218127417502200BIB027","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-55239-2"},{"key":"S0218127417502200BIB028","doi-asserted-by":"publisher","DOI":"10.1007\/BF01443420"},{"key":"S0218127417502200BIB029","doi-asserted-by":"publisher","DOI":"10.1109\/TCS.1986.1085855"},{"key":"S0218127417502200BIB030","doi-asserted-by":"publisher","DOI":"10.1142\/9789814503372_0001"},{"key":"S0218127417502200BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-2421-9"},{"key":"S0218127417502200BIB032","first-page":"361","volume":"79","author":"Le Corbeiller Ph.","year":"1936","journal-title":"J. Instit. Electric. Engin."},{"key":"S0218127417502200BIB033","doi-asserted-by":"crossref","first-page":"7219","DOI":"10.1103\/PhysRevE.63.016206","volume":"63","author":"Letellier C.","year":"2000","journal-title":"Phys. Rev. E"},{"key":"S0218127417502200BIB034","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0469(1963)020<0130:DNF>2.0.CO;2"},{"key":"S0218127417502200BIB035","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(79)90255-X"},{"key":"S0218127417502200BIB036","doi-asserted-by":"publisher","DOI":"10.1063\/1.2401060"},{"key":"S0218127417502200BIB038","doi-asserted-by":"publisher","DOI":"10.1007\/BF01940759"},{"key":"S0218127417502200BIB039","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.78.026406"},{"key":"S0218127417502200BIB040","volume-title":"M\u00e9thodes Nouvelles de la M\u00e9canique C\u00e9leste","author":"Poincar\u00e9 H.","year":"1892"},{"key":"S0218127417502200BIB041","doi-asserted-by":"publisher","DOI":"10.1038\/srep08447"},{"key":"S0218127417502200BIB042","first-page":"188","volume":"6","author":"Righi A.","year":"1902","journal-title":"Rendiconto delle sessioni dell\u2019Accademia delle scienze del Istituto di Bologna"},{"key":"S0218127417502200BIB043","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127400001638"},{"key":"S0218127417502200BIB044","volume-title":"A Treatise on the Stability of a Given State of Motion: Particularly Steady Motion","author":"Routh E. J.","year":"1877"},{"key":"S0218127417502200BIB045","doi-asserted-by":"publisher","DOI":"10.1007\/BF01646553"},{"key":"S0218127417502200BIB046","first-page":"78","volume":"6","author":"Sandri M.","year":"1996","journal-title":"Mathematica J."},{"key":"S0218127417502200BIB047","first-page":"163","volume":"6","author":"Shilnikov L. P.","year":"1965","journal-title":"Sov. Math. Dokl."},{"key":"S0218127417502200BIB048","first-page":"54","volume":"8","author":"Shilnikov L. P.","year":"1967","journal-title":"Sov. Math. Dokl."},{"key":"S0218127417502200BIB049","first-page":"460","author":"Thompson S.","year":"1892","journal-title":"The Electrician"},{"key":"S0218127417502200BIB050","doi-asserted-by":"publisher","DOI":"10.1038\/120363a0"},{"key":"S0218127417502200BIB051","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(85)90011-9"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127417502200","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:37:22Z","timestamp":1565116642000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417502200"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,30]]},"references-count":49,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2018,1,28]]},"published-print":{"date-parts":[[2017,12,30]]}},"alternative-id":["10.1142\/S0218127417502200"],"URL":"https:\/\/doi.org\/10.1142\/s0218127417502200","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,30]]}}}