含两时滞企业竞争与合作模型的全局吸引性

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

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。

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.