Bifurcation control of a delayed fractional-order prey-predator model with cannibalism and disease.

In this paper, the bifurcation control for a fractional-order delayed prey-predator system with disease and cannibalism is investigated. Firstly, the existence, uniqueness and non-negativity of the solutions are studies, and the stability of equilibrium points are discussed. Next, taking time delay as the bifurcation parameter, the conditions of creation for Hopf bifurcation are confirmed. Then, two feedback controllers are introduced, which successfully control the Hopf bifurcation, and bifurcation control of the two controllers are simply compared theoretically. Finally, numerical simulations show that cannibalism has an significant influence in controlling the stability of the model, and when the parameters are appropriate, the disease can be removed. Meanwhile, the feedback controllers can control the bifurcation well. In general, the control effect of time-delay feedback controller should be better than that of traditional feedback controller. However, we found that the control effect of the traditional feedback controller is better than the time-delay feedback controller, the control effect completely depends on the selection of parameters. [ABSTRACT FROM AUTHOR]