Dynamics of a Leslie-Gower predator-prey system with cross-diffusion
A Leslie–Gower predator–prey system with cross-diffusion subject to Neumann boundary conditions is considered. The global existence and boundedness of solutions are shown. Some sufficient conditions ensuring the existence of nonconstant solutions are obtained by means of the Leray–Schauder degree th...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Szeged
2020-11-01
|
| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7755 |
| _version_ | 1797830524962603008 |
|---|---|
| author | Rong Zou Shangjiang Guo |
| author_facet | Rong Zou Shangjiang Guo |
| author_sort | Rong Zou |
| collection | DOAJ |
| description | A Leslie–Gower predator–prey system with cross-diffusion subject to Neumann boundary conditions is considered. The global existence and boundedness of solutions are shown. Some sufficient conditions ensuring the existence of nonconstant solutions are obtained by means of the Leray–Schauder degree theory. The local and global stability of the positive constant steady-state solution are investigated via eigenvalue analysis and Lyapunov procedure. Based on center manifold reduction and normal form theory, Hopf bifurcation direction and the stability of bifurcating time-periodic solutions are investigated and a normal form of Bogdanov-Takens bifurcation is determined as well. |
| first_indexed | 2024-04-09T13:37:29Z |
| format | Article |
| id | doaj.art-97d94499c0954746a87523d84aaac7cd |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:37:29Z |
| publishDate | 2020-11-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-97d94499c0954746a87523d84aaac7cd2023-05-09T07:53:10ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752020-11-0120206513310.14232/ejqtde.2020.1.657755Dynamics of a Leslie-Gower predator-prey system with cross-diffusionRong Zou0Shangjiang Guo1School of Information and Statistics, Guangxi University of Finance and Economics, Nanning, P.R. ChinaSchool of Mathematics and Physics, China University of Geosciences, Wuhan, Hubei, P. R. ChinaA Leslie–Gower predator–prey system with cross-diffusion subject to Neumann boundary conditions is considered. The global existence and boundedness of solutions are shown. Some sufficient conditions ensuring the existence of nonconstant solutions are obtained by means of the Leray–Schauder degree theory. The local and global stability of the positive constant steady-state solution are investigated via eigenvalue analysis and Lyapunov procedure. Based on center manifold reduction and normal form theory, Hopf bifurcation direction and the stability of bifurcating time-periodic solutions are investigated and a normal form of Bogdanov-Takens bifurcation is determined as well.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7755cross-diffusionpredator–prey systemglobal existencestabilityhopf bifurcationbogdanov–takens bifurcation |
| spellingShingle | Rong Zou Shangjiang Guo Dynamics of a Leslie-Gower predator-prey system with cross-diffusion Electronic Journal of Qualitative Theory of Differential Equations cross-diffusion predator–prey system global existence stability hopf bifurcation bogdanov–takens bifurcation |
| title | Dynamics of a Leslie-Gower predator-prey system with cross-diffusion |
| title_full | Dynamics of a Leslie-Gower predator-prey system with cross-diffusion |
| title_fullStr | Dynamics of a Leslie-Gower predator-prey system with cross-diffusion |
| title_full_unstemmed | Dynamics of a Leslie-Gower predator-prey system with cross-diffusion |
| title_short | Dynamics of a Leslie-Gower predator-prey system with cross-diffusion |
| title_sort | dynamics of a leslie gower predator prey system with cross diffusion |
| topic | cross-diffusion predator–prey system global existence stability hopf bifurcation bogdanov–takens bifurcation |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7755 |
| work_keys_str_mv | AT rongzou dynamicsofalesliegowerpredatorpreysystemwithcrossdiffusion AT shangjiangguo dynamicsofalesliegowerpredatorpreysystemwithcrossdiffusion |