Volume 2, Issue 3
Qualitative Analysis of a Predator-Prey System with Ratio-Dependent and Modified Leslie-Gower Functional Response

Jie Song

J. Nonl. Mod. Anal., 2 (2020), pp. 317-332.

Published online: 2021-04

[An open-access article; the PDF is free to any online user.]

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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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@Article{JNMA-2-317, author = {Song , Jie}, title = {Qualitative Analysis of a Predator-Prey System with Ratio-Dependent and Modified Leslie-Gower Functional Response}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {2}, number = {3}, pages = {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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2020.317}, url = {http://global-sci.org/intro/article_detail/jnma/18813.html} }
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 -

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.

Song , Jie. (2021). Qualitative Analysis of a Predator-Prey System with Ratio-Dependent and Modified Leslie-Gower Functional Response. Journal of Nonlinear Modeling and Analysis. 2 (3). 317-332. doi:10.12150/jnma.2020.317
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