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Mathematical Problems in Engineering
Volume 2015, Article ID 917137, 7 pages
Research Article

Chaotification for a Class of Delay Difference Equations Based on Snap-Back Repellers

1College of Control Science and Engineering, Shandong University, Jinan, Shandong 250061, China
2School of Science, Shandong Jianzhu University, Jinan, Shandong 250101, China
3Department of Public Foundation, Shandong Radio and TV University, Jinan, Shandong 250010, China

Received 29 April 2015; Accepted 12 July 2015

Academic Editor: Xinguang Zhang

Copyright © 2015 Zongcheng Li 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 study the chaotification problem for a class of delay difference equations by using the snap-back repeller theory and the feedback control approach. We first study the stability and expansion of fixed points and establish a criterion of chaos. Then, based on this criterion of chaos and the feedback control approach, we establish a chaotification scheme such that the controlled system is chaotic in the sense of both Devaney and Li-Yorke when the parameters of this system satisfy some mild conditions. For illustrating the theoretical result, we give some computer simulations.