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<p>Based on ecology theory, a enterprise cluster model has been modeled which describes the competition and cooperation of enterprises cluster in real economic environments. Initially, we deal with the existence, uniqueness and stochastically ultimate boundedness of the positive solution to the model. Subsequently, we obtain the sufficient conditions which lead to the extinction of the enterprise. The presence of a stationary distribution is confirmed by the use of Lyapunov function. For enterprise cluster model, the stationary distribution indicates that the enterprises will persist over the long term. Finally, three numerical examples are provided to support and illustrate our main results, offering practical insights into the dynamical properties of the model. This work contributes to the development of more accurate competition and cooperation models that can support the healthy and sustainable development of enterprises.</p>

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Dynamics of a delay enterprise cluster model with environmental stochasticity

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月10日

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  • Chun Peng,
  • Xiaoliang Li,
  • Famei Zheng,
  • Haiqing Du

摘要

Based on ecology theory, a enterprise cluster model has been modeled which describes the competition and cooperation of enterprises cluster in real economic environments. Initially, we deal with the existence, uniqueness and stochastically ultimate boundedness of the positive solution to the model. Subsequently, we obtain the sufficient conditions which lead to the extinction of the enterprise. The presence of a stationary distribution is confirmed by the use of Lyapunov function. For enterprise cluster model, the stationary distribution indicates that the enterprises will persist over the long term. Finally, three numerical examples are provided to support and illustrate our main results, offering practical insights into the dynamical properties of the model. This work contributes to the development of more accurate competition and cooperation models that can support the healthy and sustainable development of enterprises.