On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nos,-Hoover oscillator

Autor(es)

Messias, Marcelo ^[1] ; Reinol, Alisson C. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Paulista UNESP, Dept Matemat & Comp, Fac Ciencias & Tecnol, Presidente Prudente, SP - Brazil

^[2] Univ Estadual Paulista UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: NONLINEAR DYNAMICS; v. 92, n. 3, p. 1287-1297, MAY 2018.
• Citações Web of Science: 1

Resumo

We consider the well-known Sprott A system, which is a special case of the widely studied Nos,-Hoover oscillator. The system depends on a single real parameter a, and for suitable choices of the parameter value, it is shown to present chaotic behavior, even in the absence of an equilibrium point. In this paper, we prove that, for the Sprott A system has neither invariant algebraic surfaces nor polynomial first integrals. For small, by using the averaging method we prove the existence of a linearly stable periodic orbit, which bifurcates from a non-isolated zero-Hopf equilibrium point located at the origin. Moreover, we show numerically the existence of nested invariant tori surrounding this periodic orbit. Thus, we observe that these dynamical elements and their perturbation play an important role in the occurrence of chaotic behavior in the Sprott A system. (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: 13/26602-7 - Integrabilidade e dinâmica global de campos vetoriais quadráticos definidos no R^3 com superfícies Quádricas invariantes
• Beneficiário: Alisson de Carvalho Reinol
• Modalidade de apoio: Bolsas no Brasil - Doutorado