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<p>The paper studies the global dynamics of an abstract higher-order fuzzy difference equation. More precisely, we prove the existence of positive solutions of this equation. We obtain the criteria in order that the equation has a unique global attractor equilibrium point. Sufficient conditions for asymptotic stability are also presented in the case of homogeneous functions. Finally, we give some examples with their numerical simulations to highlight the effectiveness of the obtained results.</p>

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On the global dynamics of an abstract higher-order fuzzy difference equation

  • 期刊论文

  • 发表日期：

    2026年2月21日

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  • Imane Dekkar,
  • Nouressadat Touafek,
  • Michal Fečkan,
  • Yasin Yazlik,
  • Sevda Atpinar

摘要

The paper studies the global dynamics of an abstract higher-order fuzzy difference equation. More precisely, we prove the existence of positive solutions of this equation. We obtain the criteria in order that the equation has a unique global attractor equilibrium point. Sufficient conditions for asymptotic stability are also presented in the case of homogeneous functions. Finally, we give some examples with their numerical simulations to highlight the effectiveness of the obtained results.