  In this paper, the dynamics of a Leslie-Gower type predator-prey system with
herd behavior and constant harvesting in prey are investigated. Earlier work
has shown that the herd behavior in prey merely induces a supercritical Hopf
bifurcation in the classic Leslie-Gower predator-prey system in the absence of
harvesting. However, the work in this paper shows that the presence of herd
behavior and constant harvesting in prey can give rise to numerous kinds of
bifurcation at the non-hyperbolic equilibria in the classic Leslie-Gower
predator-prey system such as two saddle-node bifurcations and one
Bogdanov-Takens bifurcation of codimension two at the degenerate equilibria and
one degenerate Hopf bifurcation of codimension three at the weak focus. Hence,
the research results reveal that the herd behavior and constant harvesting in
prey have a strong influence on the dynamics and also contribute to promoting
the ecological diversity and maintaining the long-term economic benefits.
