Qualitative Analysis of a Predator-Prey System with Ratio-Dependent and Modified Leslie-Gower Functional Response
Year: 2020
Author: Jie Song
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 3 : pp. 317–332
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2020.317
Journal of Nonlinear Modeling and Analysis, Vol. 2 (2020), Iss. 3 : pp. 317–332
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Predator-prey model Modified Leslie-Gower functional response Stability Nonconstant positive stationary solution.