TY - JOUR
T1 - Qualitative Analysis of a Predator-Prey System with Ratio-Dependent and Modified Leslie-Gower Functional Response
AU - Song , Jie
JO - Journal of Nonlinear Modeling and Analysis
VL - 3
SP - 317
EP - 332
PY - 2021
DA - 2021/04
SN - 2
DO - http://doi.org/10.12150/jnma.2020.317
UR - https://global-sci.org/intro/article_detail/jnma/18813.html
KW - Predator-prey model, Modified Leslie-Gower functional response,
Stability, Nonconstant positive stationary solution.
AB - <p style="text-align: justify;">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 stationary 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.</p>