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| Content Provider | Springer Nature Link |
|---|---|
| Author | Zhang, Jia Fang Li, Wan Tong Yan, Xiang Ping |
| Copyright Year | 2010 |
| Abstract | This paper is concerned with a two-species predator-prey reaction-diffusion system with Beddington-DeAngelis functional response and subject to homogeneous Neumann boundary conditions. By linearizing the system at the positive constant steady-state solution and analyzing the associated characteristic equation in detail, the asymptotic stability of the positive constant steady-state solution and the existence of local Hopf bifurcations are investigated. Also, it is shown that the appearance of the diffusion and homogeneous Neumann boundary conditions can lead to the appearance of codimension two Bagdanov-Takens bifurcation. Moreover, by applying the normal form theory and the center manifold reduction for partial differential equations (PDEs), the explicit algorithm determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions is given. Finally, numerical simulations supporting the theoretical analysis are also included. |
| Ending Page | 104 |
| Page Count | 14 |
| Starting Page | 91 |
| File Format | |
| ISSN | 01678019 |
| e-ISSN | 15729036 |
| Journal | Acta Applicandae Mathematica |
| Issue Number | 1 |
| Volume Number | 115 |
| Language | English |
| Publisher | Springer Netherlands |
| Publisher Date | 2010-11-17 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Population dynamics (general) Stability Bogdanov-Takens bifurcation Theoretical, Mathematical and Computational Physics Bifurcation Mathematics Statistical Physics, Dynamical Systems and Complexity Computer Science Mechanics Reaction-diffusion equations Diffusion Hopf bifurcation Predator-prey system |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
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