Artículos de revistas
On the integrability and the zero-Hopf bifurcation of a Chen-Wang differential system
Date
2015-04Registration in:
Nonlinear Dynamics, Dordrecht, v. 80, n. 1-2, p. 353-361, Apr. 2015
0924-090X
10.1007/s11071-014-1873-4
Author
Llibre, Jaume
Oliveira, Regilene Delazari dos Santos
Valls, Claudia
Institutions
Abstract
The first objective of this paper was to study the Darboux integrability of the polynomial differential system
'X PONTO' = y, 'Y PONTO' = z, 'Z PONTO' = −y − 'X POT.2' − xz + 3'Y POT.2' + a,
and the second one is to show that for a > 0 sufficiently small this model exhibits two small amplitude periodic solutions that bifurcate from a zero-Hopf equilibrium point localized at the origin of coordinates when a = 0. We note that this polynomial differential system introduced by Chen and Wang (Nonlinear Dyn 71:429–436, 2013) is relevant in the sense that it is the first system in 'R POT.3' exhibiting chaotic motion without having equilibria.