Stability and bifurcation control of a delayed fractional eco-epidemiological system with saturated incidence

Abstract

This paper proposes a delayed feedback control strategy for a fractional ecological infectious disease system with infected predators. Firstly, for the uncontrolled system, the stability of each equilibrium is discussed. Choosing the gestational delay as the branching parameter, the conditions of Hopf bifurcation are given at the positive equilibrium. The results show that the stable domain for the fractional system is larger than that for the integer-order system. Secondly, for the controlled system, the effects of gestational delay and feedback delay on the induction of the Hopf bifurcation are investigated, respectively. In addition, we find that the feedback gain coefficient also changes the critical value at which Hopf bifurcation occurs. Selecting a suitable feedback controller can effectively extend the stable domain of the system compared to the control-free system. Finally, the accuracy and effectiveness of the delay feedback controller in controlling the bifurcation are verified through numerical simulations.

Keywords

• Fractional system
• Hopf bifurcation
• Time delay
• Feedback controller
• Stability