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<p>In the present paper we study the existence and stability problems of positive periodic solutions to a Gilpin–Ayala competitive model with periodic coefficients on time scales. Firstly, based on Schauder’s fixed theorem, some sufficient conditions for the existence of positive periodic solution to the considered system are obtained. Furthermore, we establish asymptotic behavior by using the existence of periodic solutions. Since the considered system is based on an arbitrary time scale, our results are applicable to both discrete and continuous scenarios. We provide a specific example to verify the above results.</p>

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Dynamical behaviors of Gilpin–Ayala competitive model with periodic coefficients on time scales

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月3日

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  • Shihong Zhu,
  • Xiaoliang Li,
  • Bo Du

摘要

In the present paper we study the existence and stability problems of positive periodic solutions to a Gilpin–Ayala competitive model with periodic coefficients on time scales. Firstly, based on Schauder’s fixed theorem, some sufficient conditions for the existence of positive periodic solution to the considered system are obtained. Furthermore, we establish asymptotic behavior by using the existence of periodic solutions. Since the considered system is based on an arbitrary time scale, our results are applicable to both discrete and continuous scenarios. We provide a specific example to verify the above results.