Dynamical behaviors and chaos control in a discrete functional response model

In this paper, the dynamical behaviors and chaos control are investigated in a discrete functional response model. It is verified that there are phenomena of the transcritical bifurcation, flip bifurcation, Hopf bifurcation types and chaos in the sense of Marotto’s definition. Specifically, a controller is designed to stabilize the chaotic orbits and enable them to be an ideal target one (i.e., an unstable fixed point of the chaotic system). Finally, numerical simulations not only show the consistency with theoretical analysis but also exhibit the complex dynamical behaviors.