Transport, escape of particles and dynamical properties of some non-linear mappings
Statistical and dynamical properties of time-dependent systems
Bifurcation of invariant tori of differential systems via higher order averaging t...
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Author(s): |
Total Authors: 2
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Affiliation: | [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
Total Affiliations: 2
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Document type: | Journal article |
Source: | NONLINEAR DYNAMICS; v. 92, n. 3, p. 1287-1297, MAY 2018. |
Web of Science Citations: | 1 |
Abstract | |
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) | |
FAPESP's process: | 13/24541-0 - Ergodic and qualitative theory of dynamical systems |
Grantee: | Claudio Aguinaldo Buzzi |
Support Opportunities: | Research Projects - Thematic Grants |
FAPESP's process: | 13/26602-7 - Integrability and global dynamics of quadratic vector fields defined on R3 with Quadrics as invariant surfaces |
Grantee: | Alisson de Carvalho Reinol |
Support Opportunities: | Scholarships in Brazil - Doctorate |