Comment on "Sil'nikov chaos of the Liu system" [Chaos 18, 013113 (2008)].
In the referenced paper, the authors use the undetermined coefficient method to prove analytically the existence of homoclinic and heteroclinic orbits in a Lorenz-like system. If the proof was correct, the existence of horseshoe chaos would be guaranteed via the Sil'nikov criterion. However, we hereby show that their demonstration is incorrect for two reasons. On the one hand, they wrongly use a symmetry the Lorenz-like system exhibits. On the other hand, they try to find structurally unstable global bifurcations by means of a series that is uniformly convergent in an open set of the parameter space: this would imply that the dynamical object they have found is structurally stable.
Department of Mathematics, Facultad de Ciencias Experimentales, University of Huelva, Avda. Tres de Marzo s/n, 21071 Huelva, Spain. algaba@uhu.es
Antonio
A
Algaba
Fernando
F
Fernández-Sánchez
Manuel
M
Merino
Alejandro J
AJ
Rodríguez-Luis