Comment on ‘Šilnikov-type orbits of Lorenz-family systems’ [Physica A 375 (2007) 438–446]

In the commented paper, the authors consider a four-parameter family of three-dimensional autonomous systems that includes the widely studied systems of Lorenz, Chen and Lü. Their goal is to rigorously prove the existence of Šilnikov chaos in this Lorenz-family via the Šilnikov criterion. They use an undetermined coefficient method to demonstrate the presence of heteroclinic orbits. In this comment we point out that their analysis is erroneous. The odd function they consider for the first component of the Šilnikov heteroclinic orbit cannot represent such global connection. Thus, the main result of their paper, Theorem 2, is incorrect.