This paper is concerned with a predator-prey model with prey-taxis and
linear prey harvesting under the homogeneous Neumann boundary condition.
The stability of the unique positive constant solution of the
predator-prey model without prey-taxis is derived. Also, the emergence
of Hopf bifurcation is concluded by choosing the proper Hopf bifurcation
parameters. Moreover, the existence of non-constant positive steady
states is investigated by the introduce of prey-taxis. The conclusions
show that prey harvesting and prey-taxis can enrich the dynamics.