Coexistence of Stability and Chaos in a Class of Difference Equations with Two Delays

• Wei Liang ^[1] ; Yongjun Zhang ^[1] ; Xuanxuan Zhang ^[1]
  1. [1] Henan Polytechnic University

     Henan Polytechnic University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
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• Resumen

  • Stability and chaos of a class of difference equations with two arbitrary delays are considered in this paper. Asymptotic stability of the fixed point of the equation is obtained.

    Meanwhile, three criteria of both Devaney chaos and Li–Yorke chaos are established and rigorous proofs of the chaos are presented. To further verify the correctness and feasibility of the theoretical results, three examples are provided. One is about asymptotic stability, and the others are related to chaos, moreover, their dynamical behavior and trend of the largest Lyapunov exponents (LE) are provided, and the positivity of LE confirms the existence of chaos.