In this paper we study the complex dynamics of predator-prey systems with nonmonotonic
functional response and harvesting. When the harvesting is constant-yield for prey, it is
shown that various kinds of bifurcations, such as saddle-node bifurcation, degenerate Hopf
bifurcation, and Bogdanov-Takens bifurcation, occur in the model as parameters vary. The
existence of two limit cycles and a homoclinic loop is established by numerical
simulations. When the harvesting is seasonal for both species, sufficient conditions for
the existence of an asymptotically stable periodic solution and bifurcation of a stable
periodic orbit into a stable invariant torus of the model are given. Numerical simulations
are carried out to demonstrate the existence of bifurcation of a stable periodic orbit
into an invariant torus and transition from invariant tori to periodic solutions,
respectively, as the amplitude of seasonal harvesting increases.