Hopf bifurcation for a delayed predator–prey diffusion system with Dirichlet boundary condition
| Autor: | Hai-Feng Huo, Hong Xiang, Zhan-Ping Ma |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Hopf bifurcation
Period-doubling bifurcation Applied Mathematics 010102 general mathematics Mathematical analysis Saddle-node bifurcation Bifurcation diagram 01 natural sciences 010101 applied mathematics Computational Mathematics symbols.namesake Transcritical bifurcation Dirichlet boundary condition symbols 0101 mathematics Infinite-period bifurcation Bifurcation Mathematics |
| Zdroj: | Applied Mathematics and Computation. 311:1-18 |
| ISSN: | 0096-3003 |
| DOI: | 10.1016/j.amc.2017.05.012 |
| Popis: | A delayed predator–prey diffusion system with Beddington–DeAngelis functional response under Dirichlet boundary condition is investigated. The existence and stability of the positive spatially nonhomogeneous steady-state solution are obtained via the implicit function theorem. Moreover, taking feedback time delay τ as the bifurcation parameter, Hopf bifurcation near the positive steady-state solution is proved to occur at a sequence of critical values, we can show that feedback time delay can induce nonhomogeneous periodic oscillatory patterns. The direction of Hopf bifurcation is forward when parameter m in model (1.2) is sufficiently large. Numerical simulations and numerical solutions are presented to illustrate our theoretical results. |
| Databáze: | OpenAIRE |
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