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<p>We study the global dynamics of a rational difference equation with higher order, which includes many rational difference equations as its special cases. By some complicate computations and mathematical skills, we show that its unique nonnegative fixed point is globally attractive. As application, our results not only improve many known ones, but also solve several “Open Problems and Conjectures” given by Professors Ladas and Camouzis, et al.</p>

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Global attractivity of a rational difference equation with higher order and its application to several conjectures

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Xian-yi Li,
  • Dan-yang Li

摘要

We study the global dynamics of a rational difference equation with higher order, which includes many rational difference equations as its special cases. By some complicate computations and mathematical skills, we show that its unique nonnegative fixed point is globally attractive. As application, our results not only improve many known ones, but also solve several “Open Problems and Conjectures” given by Professors Ladas and Camouzis, et al.