Existence of chaos for a simple delay difference equation

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• 作者：Zongcheng Li (1) (2)
  Xiaoying Zhu (1)
  
  1. School of Science ; Shandong Jianzhu University ; Jinan ; Shandong ; 250101 ; China
  2. College of Control Science and Engineering ; Shandong University ; Jinan ; Shandong ; 250061 ; China
  
• 关键词：delay ; snap ; back repeller ; chaos in the sense of Devaney ; chaos in the sense of Li ; Yorke
• 刊名：Advances in Difference Equations
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,643 KB
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• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper, we study the existence of chaos for a simple delay difference equation. By using the snap-back repeller theory, we prove that the 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 two computer simulations.