GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES
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Data
2012-06-01
Autores
Llibre, Jaume
Messias, Marcelo [UNESP]
Da Silva, Paulo Ricardo [UNESP]
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Editor
World Scientific Publ Co Pte Ltd
Resumo
In this paper, we perform a global analysis of the dynamics of the Chen system(x) over dot = a(y - x), (y) over dot = (c - a)x - xz + cy, (z) over dot = xy - bz,where (x, y, z) is an element of R-3 and (a, b, c) is an element of R-3. We give the complete description of its dynamics on the sphere at infinity. For six sets of the parameter values, the system has invariant algebraic surfaces. In these cases, we provide the global phase portrait of the Chen system and give a complete description of the alpha- and omega-limit sets of its orbits in the Poincare ball, including its boundary S-2, i.e. in the compactification of R-3 with the sphere S-2 of infinity. Moreover, combining the analytical results obtained with an accurate numerical analysis, we prove the existence of a family with infinitely many heteroclinic orbits contained on invariant cylinders when the Chen system has a line of singularities and a first integral, which indicates the complicated dynamical behavior of the Chen system solutions even in the absence of chaotic dynamics.
Descrição
Palavras-chave
Chen system, integrability, Poincare compactification, dynamics at infinity, heteroclinic orbits, singularly degenerate heteroclinic cycles, invariant manifolds
Como citar
International Journal of Bifurcation and Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 22, n. 6, p. 17, 2012.