Table of Contents
Journal of Discrete Mathematics
Volume 2014, Article ID 538423, 5 pages
http://dx.doi.org/10.1155/2014/538423
Research Article

Chaotification for Partial Difference Equations via Controllers

1School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, China
2Department of Mathematics, Shandong University, Jinan, Shandong 250100, China
3Department of Mathematics, Shandong Jianzhu University, Jinan, Shandong 250100, China

Received 1 December 2013; Accepted 22 January 2014; Published 13 March 2014

Academic Editor: Zhan Zhou

Copyright © 2014 Wei Liang 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.

Linked References

  1. H. Gang and Q. Z. Qu Zhilin, “Controlling spatiotemporal chaos in coupled map lattice systems,” Physical Review Letters, vol. 72, no. 1, pp. 68–71, 1994. View at Publisher · View at Google Scholar · View at Scopus
  2. F. H. Willeboordse, “Time-delayed map as a model for open fluid flow,” Chaos, vol. 2, no. 3, pp. 423–426, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. G. Chen and S. T. Liu, “On spatial periodic orbits and spatial chaos,” International Journal of Bifurcation and Chaos, vol. 13, no. 4, pp. 935–941, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. G. Chen, C. Tian, and Y. Shi, “Stability and chaos in 2-D discrete systems,” Chaos, Solitons & Fractals, vol. 25, no. 3, pp. 637–647, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Y. Shi, “Chaos in first-order partial difference equations,” Journal of Difference Equations and Applications, vol. 14, no. 2, pp. 109–126, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. Shi, P. Yu, and G. Chen, “Chaotification of discrete dynamical systems in Banach spaces,” International Journal of Bifurcation and Chaos, vol. 16, no. 9, pp. 2615–2636, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. W. Liang, Y. Shi, and C. Zhang, “Chaotification for a class of first-order partial difference equations,” International Journal of Bifurcation and Chaos, vol. 18, no. 3, pp. 717–733, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Z. Li, “Chaotification for linear delay difference equations,” Advances in Difference Equations, vol. 2013, article 459, 11 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. T. Y. Li and J. A. Yorke, “Period three implies chaos,” The American Mathematical Monthly, vol. 82, no. 10, pp. 985–992, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley Studies in Nonlinearity, Addison-Wesley, Redwood City, Calif, USA, 2nd edition, 1989. View at MathSciNet
  11. W. Huang and X. Ye, “Devaney's chaos or 2-scattering implies Li-Yorke's chaos,” Topology and Its Applications, vol. 117, no. 3, pp. 259–272, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. S. Cheng, Partial Difference Equations, vol. 3 of Advances in Discrete Mathematics and Applications, Taylor & Francis, London, UK, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet