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

Author

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  • Zongcheng Li
  • Shutang Liu
  • Wei Li
  • Qingli Zhao

Abstract

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.

Suggested Citation

  • Zongcheng Li & Shutang Liu & Wei Li & Qingli Zhao, 2015. "Chaotification for a Class of Delay Difference Equations Based on Snap-Back Repellers," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, October.
    • Handle: RePEc:hin:jnlmpe:917137
    DOI: 10.1155/2015/917137
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    Cited by:

    1. Liang, Wei & Lv, Xiaolin, 2022. "Li-Yorke chaos in a class of controlled delay difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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