For the Ekpyrotic universe, the entropic mechanisms with minimal couplings, which have been used to generate nearly scale invariant primordial perturbations, was proved to be unstable. To overcome this difficulty, some non-minimal coupling entropic models were proposed. In this paper we extend these studies to the cases where all the scalar fields have non-standard kinetic terms. We first prove that in these general cases, without non-minimal couplings the entropic models are still unstable. The condition for the stability conflicts with the requirement for achieving scale invariant perturbations. Then we study the non-minimal coupling models and show that at least for some simple cases these models are stable and able to generate the primordial perturbations consistent with current observations. (C) 2015 The Author. Published by Elsevier B. V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).