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New insights on bifurcation in a fractional-order delayed competition and cooperation model of two enterprises
Changjin Xu,Maoxin Liao,Peiluan Li,Shuai Yuan
Keywords:Fractional order competition and cooperation model; Enterprise; Hopf bifurcation; Stability; Delay
Abstract:
      Over the past decades, many authors establish various kinds of competition and cooperation models of two enterprises to analyze the dynamic interaction. However, they are only concerned with integer-order differential equation models, while the reports on fractional-order ones are very rare. In this article, based on the earlier studies, we propose a new fractional-order delayed competition and cooperation model of two enterprises. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equation of involved model, we establish some new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed competition and cooperation model of two enterprises. The research indicates that different delays have different effect on the stability and Hopf bifurcation of involved model. The impact of the fractional order on the stability and Hopf bifurcation of involved model is displayed. To check the correctness of theoretical analysis, we implement some computer simulations.