{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T09:31:47Z","timestamp":1659087107447},"reference-count":19,"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":[[2018,12,30]]},"abstract":"<jats:p> According to the theory of stable and unstable manifolds of an equilibrium point, we firstly find out some geometrical properties of orbits on the stable and unstable manifolds of a saddle point under some brief conditions of nonlinear terms composed of polynomials for [Formula: see text]-dimensional time continuous system. These properties show that the orbits on stable and unstable manifolds of the saddle point will stay on the corresponding stable and unstable subspaces in the [Formula: see text]-neighborhood of the saddle point. Furthermore, the necessary conditions of existence for orbit homoclinic to a saddle point are exposed. Some examples including homoclinic bifurcation are given to indicate the application of the results. Finally, the conclusions are presented. <\/jats:p>","DOI":"10.1142\/s0218127418501699","type":"journal-article","created":{"date-parts":[[2019,1,8]],"date-time":"2019-01-08T02:33:12Z","timestamp":1546914792000},"page":"1850169","source":"Crossref","is-referenced-by-count":1,"title":["Study on the Geometrical Properties and Existence of Orbit Homoclinic to a Saddle Point in n-Dimensional Autonomous Vector Field with Polynomials"],"prefix":"10.1142","volume":"28","author":[{"given":"Lingli","family":"Xie","sequence":"first","affiliation":[{"name":"Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,1,7]]},"reference":[{"key":"S0218127418501699BIB001","doi-asserted-by":"publisher","DOI":"10.1137\/12087654X"},{"key":"S0218127418501699BIB002","doi-asserted-by":"publisher","DOI":"10.1063\/1.3339819"},{"key":"S0218127418501699BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127409023779"},{"key":"S0218127418501699BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-3126-1"},{"key":"S0218127418501699BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-015-9437-y"},{"key":"S0218127418501699BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8928(01)00004-1"},{"key":"S0218127418501699BIB007","first-page":"49","volume":"8","author":"Leonov G. A.","year":"2008","journal-title":"Nonlin. Dyn. Syst. Th."},{"key":"S0218127418501699BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2012.07.003"},{"key":"S0218127418501699BIB009","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127413500582"},{"key":"S0218127418501699BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-014-1622-8"},{"key":"S0218127418501699BIB011","doi-asserted-by":"publisher","DOI":"10.3934\/cpaa.2017111"},{"key":"S0218127418501699BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127411030039"},{"key":"S0218127418501699BIB013","first-page":"163","volume":"6","author":"Shi\u2019lnikov L. P.","year":"1965","journal-title":"Sov. Math. Dokl."},{"key":"S0218127418501699BIB014","first-page":"1368","volume":"10","author":"Shi\u2019lnikov L. P.","year":"1969","journal-title":"Sov. Math."},{"key":"S0218127418501699BIB015","doi-asserted-by":"publisher","DOI":"10.1070\/SM1970v010n01ABEH001588"},{"key":"S0218127418501699BIB016","doi-asserted-by":"publisher","DOI":"10.1109\/81.246142"},{"key":"S0218127418501699BIB017","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008202529152"},{"key":"S0218127418501699BIB018","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1996.0121"},{"key":"S0218127418501699BIB019","volume-title":"Introduction to Applied Nonlinear Dynamical Systems and Chaos","author":"Wiggins S.","year":"2003","edition":"2"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127418501699","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:36:45Z","timestamp":1565138205000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127418501699"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,30]]},"references-count":19,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2019,1,7]]},"published-print":{"date-parts":[[2018,12,30]]}},"alternative-id":["10.1142\/S0218127418501699"],"URL":"https:\/\/doi.org\/10.1142\/s0218127418501699","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,30]]}}}