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Bifurcation control of a fractional-order delayed competition and cooperation model of two enterprises

Science China(Technological Sciences) 2019年第12期62卷 2130-2143页

作者： XU ChangJin LIAO MaoXin LI PeiLuan Guizhou Key Laboratory of Economics System Simulation Guizhou University of Finance and EconomicsGuiyang 50004China School of Mathematics and Physics University of Souh ChinaHengyang 421001China School of Mathematics and Statistics Henan University of Science and TechnologyLuoyang 471023China

The competition and cooperation among enterprises has become a hot topic and focus issue in today’s world. How to manage the enterprise well so as to achieve the maximum output is an important problem for enterprise managers. Optimizing output of two enterprises plays a key role in operating enterprises. Many scholars pay much attention to this aspect. However, the reports on the stability and Hopf bifurcation for fractional-order delayed competition and cooperation model of two enterprises are very few. This paper is concerned with the stability, the existence of Hopf bifurcation and the bifurcation control issue of fractionalorder delayed competition and cooperation model of two enterprises. Firstly, some new sufficient conditions that guarantee the stability and the existence of Hopf bifurcation for fractional-order delayed competition and cooperation model of two enterprises are obtained by regarding the delay as bifurcation parameter. Then a suitable time delayed feedback controller is designed to control the Hopf bifurcation for involved model. The study shows that the delay and the fractional order have an important effect on the stability and Hopf bifurcation of involved model. Some simulations justifying the validity of the derived analytical results are given. At last, we end this paper with a concise conclusion. The obtained results of this article are innovative and are of great significance in handling the competition and cooperation among enterprises.

关键词： bifurcation control competition and cooperation model enterprise stability hopf bifurcation fractional order elay

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