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- Title
Chaotic Behavior of a Generalized Sprott E Differential System.
- Authors
Oliveira, Regilene; Valls, Claudia
- Abstract
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 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 where are parameters and . 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 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 sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point . We also give a complete description of its dynamics on the Poincaré sphere at infinity by using the Poincaré compactification of a polynomial vector field in , and we show that it has no first integrals in the class of Darboux functions.
- Subjects
CHAOS theory; EXTERIOR differential systems; ATTRACTORS (Mathematics); HOPF bifurcations; POINCARE maps (Mathematics); DARBOUX transformations
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2016, Vol 26, Issue 5, p-1
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127416500838