{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T13:04:04Z","timestamp":1758891844399},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> In this paper, we perform a global analysis of the dynamics of the Chen system [Formula: see text] where (x, y, z) \u2208 \u211d<jats:sup>3<\/jats:sup> and (a, b, c) \u2208 \u211d<jats:sup>3<\/jats:sup>. We give the complete description of its dynamics on the sphere at infinity. For six sets of the parameter values, the system has invariant algebraic surfaces. In these cases, we provide the global phase portrait of the Chen system and give a complete description of the \u03b1- and \u03c9-limit sets of its orbits in the Poincar\u00e9 ball, including its boundary \ud835\udd4a<jats:sup>2<\/jats:sup>, i.e. in the compactification of \u211d<jats:sup>3<\/jats:sup> with the sphere \ud835\udd4a<jats:sup>2<\/jats:sup> of infinity. Moreover, combining the analytical results obtained with an accurate numerical analysis, we prove the existence of a family with infinitely many heteroclinic orbits contained on invariant cylinders when the Chen system has a line of singularities and a first integral, which indicates the complicated dynamical behavior of the Chen system solutions even in the absence of chaotic dynamics. <\/jats:p>","DOI":"10.1142\/s0218127412501544","type":"journal-article","created":{"date-parts":[[2012,4,24]],"date-time":"2012-04-24T01:04:26Z","timestamp":1335229466000},"page":"1250154","source":"Crossref","is-referenced-by-count":27,"title":["GLOBAL DYNAMICS IN THE POINCAR\u00c9 BALL OF THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES"],"prefix":"10.1142","volume":"22","author":[{"given":"JAUME","family":"LLIBRE","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]},{"given":"MARCELO","family":"MESSIAS","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Estat\u00edstica e Computa\u00e7\u00e3o, Faculdade de Ci\u00eancias e Tecnologia, UNESP \u2013 Univ Estadual Paulista, Cx. Postal 266, 19060-900, Presidente Prudente, S\u00e3o Paulo, Brazil"}]},{"given":"PAULO","family":"RICARDO DA SILVA","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto de Bioci\u00eancias, Letras e Ci\u00eancias Exatas, UNESP \u2013 Univ Estadual Paulista, Rua C. Colombo, 2265, 15054-000, S. J. Rio Preto, S\u00e3o Paulo, Brazil"}]}],"member":"219","published-online":{"date-parts":[[2012,7,16]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.02.011"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127408022706"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127499001024"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1990-0998352-5"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s10884-004-4290-4"},{"key":"rf6","first-page":"21","volume":"41","author":"Llibre J.","journal-title":"J. Phys. A: Math. 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