Comment on “Existence of heteroclinic orbits of the Shilʼnikov type in a 3D quadratic autonomous chaotic system” [J. Math. Anal. Appl. 315 (2006) 106–119]

In the referenced paper the existence of heteroclinic orbits of Shilʼnikov type is proved by using the undetermined coefficient method, in a three-dimensional quadratic autonomous system. Here we show that the demonstration is incorrect. A misuse of a time-reversibility property leads the authors to consider an odd expression for the first component of the heteroclinic connection. It is evident that this odd expression can never represent the first component of a Shilʼnikov heteroclinic connection, an orbit which is necessarily non-symmetric.