BIFURCATION CONTROL STRATEGY FOR A DELAYED FRACTIONAL-ORDER POPULATION DYNAMICS MODEL WITH INCOMMENSURATE ORDERS

Abstract

This paper excogitates a bifurcation control strategy for a delayed fractional-order population dynamics model with incommensurate orders. First and foremost, by using stability theory of fractional differential equations, the sufficient conditions for the stability of the positive equilibrium are established. It is not difficult to find that the fractional-order system has a wider stability region than the traditional integer-order system. Second, taking time delay as bifurcation parameter, the sufficient criteria for Hopf bifurcation are obtained. In the next place, it is interesting to introduce a delayed feedback controller to guide Hopf bifurcation. The results reveal that the bifurcation dynamics of the model could be effectively controlled as long as the delay or fractional order is carefully adjusted. In conclusion, numerical simulations are carried out to confirm our theoretical results.