Stability and bifurcation control of a delayed fractional-order eco-epidemiological model with incommensurate orders

Abstract In this paper, a delayed fractional eco-epidemiological model with incommensurate orders is proposed, and a control strategy of this model is discussed. Firstly, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Secondly, under the influence of the controller, the stability and Hopf bifurcation of the system is discussed, and it is indicated that the stability of the system can be changed by increasing the feedback control delay. In particular, a separate study is carried out on the bifurcation with respect to the extended feedback delay, and the bifurcation point is calculated. At last, to support the theoretical results, some numerical simulations are depicted.