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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2022, Vol. 39 ›› Issue (3): 451-462.doi: 10.3969/j.issn.1005-3085.2022.03.009

• • 上一篇    下一篇

含两时滞企业竞争与合作模型的全局吸引性

艾合麦提·麦麦提阿吉   

  1. 新疆大学数学与系统科学学院，乌鲁木齐 830017
  • 出版日期:2022-06-15 发布日期:2022-08-15
  • 基金资助:
    国家自然科学基金 (11861063)；新疆自然科学基金 (2021D01067).

Global Attractivity of a Competition and Cooperation Model of Enterprises with Two Time Delays

MUHAMMADHAJI Ahmadjan   

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017
  • Online:2022-06-15 Published:2022-08-15
  • Supported by:
    The National Natural Science Foundation of China (11861063); the Natural Science Foundation of Xinjiang (2021D01067).

PDF (PC)

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摘要：

研究了具有两时滞的非自治企业竞争与合作动力学模型的动力学行为。应用不等式技巧和构造多重 Lyapunov 函数的方法得到了模型的最终有界性和全局吸引性的充分条件。作为所得主要结论的应用，对所研究模型的三个特殊情况进行了研究，并得到了所研究模型的最终有界性和全局吸引性的充分条件。最后，两个数值例子进一步验证了所得结论的有效性和合理性。从所得主要结论和两个数值实例可以得到，两个离散时滞影响模型全局吸引性的结论。所得主要结论改进和推广了目前已有的关于两企业竞争与合作动力学模型方面的相关研究。

关键词: 竞争与合作模型, 最终有界性, 全局吸引性, 时滞

Abstract:

This paper studies a class of non-autonomous competition and cooperation model of enterprises with two time delays. Sufficient conditions for the ultimately boundedness and global attractivity of the model are derived by using inequality techniques and the construction of multiple Lyapunov functions. As an application of the main results, also studied are three special cases of the considered model, and obtained the sufficient conditions on the ultimately boundedness and global attractivity of the considered models. Finally, two numerical examples further verified the validity and effectiveness of the obtained results. From the main results and two numerical examples, it can be concluded that the two discrete delays affect the global attractiveness of the model. The obtained results improvemed and extended the previously related studies.

Key words: competition and cooperation model, ultimately boundedness, global attractivity, time delay

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