Saddle-node bifurcation

Physics

Artificial intelligence

Nonlinear system

Hopf bifurcation

Biological applications of bifurcation theory

Period-doubling bifurcation

Controller (irrigation)

Control (management)

Bifurcation

Applied mathematics

Mathematics

Computer science

Control theory (sociology)

Transcritical bifurcation

Quantum mechanics

Agronomy

Bifurcation diagram

Biology

Applied Mathematics and Computation

This paper aims at controlling bifurcation of a fractional predator–prey system by an original extended delayed feedback controller. Firstly, some sufficient conditions of delay-induced bifurcations for such uncontrolled system are captured regarding time delay as a bifurcation parameter. Secondly, a generalised delayed feedback controller is subtly designed to control Hopf bifurcation for the proposed system. It suggests that bifurcation dynamics can be controlled efficaciously for such system by carefully adjusting extended feedback delay or fractional order so long as the other parameters are established. Thirdly, the bifurcation diagrams are meticulously plotted. The obtained results consumedly popularize the previous studies concerning bifurcation control of delayed fractional-order systems. To underline the effectiveness of the proposed control scheme, some numerical simulations are ultimately addressed.

A novel strategy of bifurcation control for a delayed fractional predator–prey model