| 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. |
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