Copyright © 2013 Lidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove that a dynamical system is chaotic in the sense of Martelli and Wiggins, when it is a transitive distributively chaotic in a sequence. Then, we give a sufficient condition for the dynamical system to be chaotic in the strong sense of Li-Yorke. We also prove that a dynamical system is distributively chaotic in a sequence, when it is chaotic in the strong sense of Li-Yorke.