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

  • ChangJin XuEmail author
  • MaoXin Liao
  • PeiLuan Li
Article
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Abstract

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 fractional-order 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.

Keywords

bifurcation control competition and cooperation model enterprise stability hopf bifurcation fractional order delay 

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Guizhou Key Laboratory of Economics System SimulationGuizhou University of Finance and EconomicsGuiyangChina
  2. 2.School of Mathematics and PhysicsUniversity of South ChinaHengyangChina
  3. 3.School of Mathematics and StatisticsHenan University of Science and TechnologyLuoyangChina

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