Bifurcations at infinity, invariant algebraic surfaces, homoclinic and heteroclinic orbits and centers of a new Lorenz-like chaotic system

Autor(es)

Gouveia, Marcio R. A. ^[1] ; Messias, Marcelo ^[2] ; Pessoa, Claudio ^[1]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista, Inst Biociencias Letras & Ciencias Exatas IBILCE, Dept Matemat, UNESP, Sao Jose Do Rio Preto, SP - Brazil

^[2] Univ Estadual Paulista, Dept Matemat & Comp, FCT, UNESP, Presidente Prudente, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR DYNAMICS; v. 84, n. 2, p. 703-713, APR 2016.
• Citações Web of Science: 2

Resumo

We present a global dynamical analysis of the following quadratic differential system , where are the state variables and a, b, d, f, g are real parameters. This system has been proposed as a new type of chaotic system, having additional complex dynamical properties to the well-known chaotic systems defined in , alike Lorenz, Rossler, Chen and other. By using the Poincar, compactification for a polynomial vector field in , we study the dynamics of this system on the Poincar, ball, showing that it undergoes interesting types of bifurcations at infinity. We also investigate the existence of first integrals and study the dynamical behavior of the system on the invariant algebraic surfaces defined by these first integrals, showing the existence of families of homoclinic and heteroclinic orbits and centers contained on these invariant surfaces. (AU)

• Processo FAPESP: 13/24541-0 - Teorias ergódica e qualitativa dos sistemas dinâmicos
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 12/18413-7 - Análise global de sistemas diferenciais polinomiais definidos no espaço R3
• Beneficiário: Marcelo Messias
• Modalidade de apoio: Auxílio à Pesquisa - Regular