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Chaotic Behavior of a Generalized Sprott E Differential System

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Autor(es):
Oliveira, Regilene [1] ; Valls, Claudia [2]
Número total de Autores: 2
Afiliação do(s) autor(es):
[1] Univ Sao Paulo, ICMC, Dept Matemat, Sao Paulo - Brazil
[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, P-1049001 Lisbon - Portugal
Número total de Afiliações: 2
Tipo de documento: Artigo Científico
Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 26, n. 5 MAY 2016.
Citações Web of Science: 0
Resumo

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 b 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 (x) over dot = ayz + b, (y) over dot = x(2) - y, (z) over dot = 1 - 4x, where a, b epsilon R are parameters and a not equal 0. 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 R-3 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 b sufficiently small this system can exhibit two limit cycles emerging from the classical Hopf bifurcation at the equilibrium point p = (1/4, 1/16, 0). We also give a complete description of its dynamics on the Poincare sphere at infinity by using the Poincare compactification of a polynomial vector field in R-3, and we show that it has no first integrals in the class of Darboux functions. (AU)

Processo FAPESP: 14/00304-2 - Singularidades de aplicações diferenciáveis: teoria e aplicações
Beneficiário:Maria Aparecida Soares Ruas
Linha de fomento: Auxílio à Pesquisa - Temático