Otro
GLOBAL DYNAMICS IN THE POINCARE BALL of THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES
Registro en:
International Journal of Bifurcation and Chaos. Singapore: World Scientific Publ Co Pte Ltd, v. 22, n. 6, p. 17, 2012.
0218-1274
10.1142/S0218127412501544
WOS:000306505900031
Autor
Llibre, Jaume
Messias, Marcelo
Da Silva, Paulo Ricardo
Resumen
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. Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)