Global dynamical aspects of a generalized Chen-Wang differential system

Autor(es)

Oliveira, Regilene ^[1] ; Valls, Claudia ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil

^[2] Univ Lisbon, Inst Super Tecn, Dept Matemat, Av Rovisco Pais, P-1049001 Lisbon - Portugal

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR DYNAMICS; v. 84, n. 3, p. 1497-1516, MAY 2016.
• Citações Web of Science: 0

Resumo

We study theoretically the global chaotic behavior of the generalized Chen-Wang differential system where are parameters and . This polynomial differential system is relevant because is the first polynomial differential system in with two parameters exhibiting chaotic motion without having equilibria. We first show that for sufficiently small it can exhibit up to three small amplitude periodic solutions that bifurcate from a zero-Hopf equilibrium point located at the origin of coordinates when . We also show that the system exhibits two limit cycles emerging from two classical Hopf bifurcations at the equilibrium points , for . We also give a complete description of its dynamics on the Poincar, sphere at infinity by using the Poincar, compactification of a polynomial vector field in , and we show that it has no first integrals neither in the class of analytic functions nor in the class of Darboux functions. (AU)

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