Journal of Applied Mathematics
Volume 2013 (2013), Article ID 212036, 4 pages
http://dx.doi.org/10.1155/2013/212036
Research Article

Chaos for Discrete Dynamical System

Lidong Wang,1,2 Heng Liu,1,2 and Yuelin Gao1

1Information and Computational Science department, Beifang University of Nationality, Yinchuan, Ningxia 750021, China
2School of Science, Dalian Nationalities University, Dalian, Liaoning 116600, China

Received 8 January 2013; Revised 1 March 2013; Accepted 2 March 2013

Academic Editor: Ezio Venturino

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.

Abstract

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.