Bifurcation analysis and hybrid control of a discrete-time predator-prey model

In this paper, a discrete-time predator-prey model with six parameters is investigated. After splitting the parameter space with respect to the number of fixed points, we obtain both transcritical bifurcation surfaces and a Neimark-Sacker bifurcation surface in the six-dimensional parameter space by the normal form method. Then we apply a hybrid control strategy to control the Neimark-Sacker bifurcation so that the positive fixed point of the controlled system is locally asymptotically stable. Numerical simulations are performed to illustrate our theoretical results.