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Such a representation of the dynamics on the manifold is obtained in terms of a simple conjugacy relation and by constructing two contracting operators. We illustrate our techniques by plotting (for specific values of the parameters) both stable and unstable manifolds displaying homoclinic intersection. Furthermore, our numerical study reveals the presence of a strange attractor included in the closure of the unstable manifold of the fixed point. <\/jats:p>","DOI":"10.1142\/s0218127421501947","type":"journal-article","created":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T08:39:21Z","timestamp":1635151161000},"source":"Crossref","is-referenced-by-count":0,"title":["Complexity in a Hybrid van der Pol System"],"prefix":"10.1142","volume":"31","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9483-6874","authenticated-orcid":false,"given":"Vincent","family":"Naudot","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shane","family":"Kepley","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Rutgers, The State University of New Jersey, New Brunswick, NJ, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William D.","family":"Kalies","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,10,25]]},"reference":[{"key":"S0218127421501947BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2014.09.023"},{"key":"S0218127421501947BIB002","doi-asserted-by":"publisher","DOI":"10.2307\/2944326"},{"key":"S0218127421501947BIB003","doi-asserted-by":"publisher","DOI":"10.1023\/A:1024467732637"},{"key":"S0218127421501947BIB004","doi-asserted-by":"publisher","DOI":"10.1512\/iumj.2003.52.2245"},{"key":"S0218127421501947BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2004.12.003"},{"key":"S0218127421501947BIB006","doi-asserted-by":"publisher","DOI":"10.1137\/070688080"},{"key":"S0218127421501947BIB007","doi-asserted-by":"publisher","DOI":"10.1137\/18M1192007"},{"key":"S0218127421501947BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2016.06.009"},{"key":"S0218127421501947BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF01022365"},{"key":"S0218127421501947BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/16M1090041"},{"volume-title":"Chebyshev Polynomials","year":"2002","author":"Handscomb D.","key":"S0218127421501947BIB012"},{"key":"S0218127421501947BIB013","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2006.6.1261"},{"key":"S0218127421501947BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/0167-2789(92)90012-C"},{"key":"S0218127421501947BIB015","doi-asserted-by":"publisher","DOI":"10.1007\/BF01608556"},{"key":"S0218127421501947BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0092042"},{"key":"S0218127421501947BIB017","first-page":"402","volume":"12","author":"Ippolito S.","year":"2016","journal-title":"Electron. 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