| In this paper, a predator-prey model with ratio-dependent and
modified Leslie-Gower functional response subject to homogeneous Neumann
boundary condition is considered. First, properties of the constant positive sta-
tionary solution are shown, including the existence, nonexistence, multiplicity
and stability. In addition, a comparatively characterization of the stability is
obtained. Moreover, the existing result of global stability is improved. Finally,
properties of nonconstant positive stationary solutions are further studied. By
a priori estimate and the theory of Leray-Schauder degree, it is shown that
nonconstant positive stationary solutions may exist when the system has two
constant positive stationary solutions. |
