Zou Rong and Guo Shangjiang: Dynamics of a Leslie-Gower predator-prey system with cross-diffusion. (2020)
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Abstract
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 timeperiodic solutions are investigated and a normal form of Bogdanov–Takens bifurcation is determined as well.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2020 |
| Number: | 65 |
| ISSN: | 1417-3875 |
| Number of Pages: | 33 |
| Language: | English |
| DOI: | 10.14232/ejqtde.2020.1.65 |
| Uncontrolled Keywords: | Hopf bifurkáció, Bogdanov-Takens bifurkáció, Differenciálegyenlet |
| Additional Information: | Bibliogr.: p. 30-33. ; ill. ; összefoglalás angol nyelven |
| Date Deposited: | 2021. Nov. 05. 12:24 |
| Last Modified: | 2021. Nov. 05. 12:24 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/73626 |
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