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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2016,5]]},"abstract":"<jats:p> A chaotic system with only one equilibrium, a stable node-focus, was introduced by Wang and Chen [2012]. This system was found by adding a nonzero constant [Formula: see text] to the Sprott E system [Sprott, 1994]. The coexistence of three types of attractors in this autonomous system was also considered by Braga and Mello [2013]. Adding a second parameter to the Sprott E differential system, we get the autonomous system [Formula: see text] where [Formula: see text] are parameters and [Formula: see text]. In this paper, we consider theoretically some global dynamical aspects of this system called here the generalized Sprott E differential system. This polynomial differential system is relevant because it is the first polynomial differential system in [Formula: see text] with two parameters exhibiting, besides the point attractor and chaotic attractor, coexisting stable limit cycles, demonstrating that this system is truly complicated and interesting. More precisely, we show that for [Formula: see text] sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point [Formula: see text]. We also give a complete description of its dynamics on the Poincar\u00e9 sphere at infinity by using the Poincar\u00e9 compactification of a polynomial vector field in [Formula: see text], and we show that it has no first integrals in the class of Darboux functions. <\/jats:p>","DOI":"10.1142\/s0218127416500838","type":"journal-article","created":{"date-parts":[[2016,5,31]],"date-time":"2016-05-31T02:25:31Z","timestamp":1464661531000},"page":"1650083","source":"Crossref","is-referenced-by-count":6,"title":["Chaotic Behavior of a Generalized Sprott E Differential System"],"prefix":"10.1142","volume":"26","author":[{"given":"Regilene","family":"Oliveira","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, ICMC \u2013 Universidade de S\u00e3o Paulo, 13566\u2013590, S\u00e3o Carlos, S\u00e3o Paulo, Brazil"}]},{"given":"Claudia","family":"Valls","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Instituto Superior T\u00e9cnico, Universidade de Lisboa, Av. 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