کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
755955 | 896090 | 2011 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Stability and global Hopf bifurcation in a delayed food web consisting of a prey and two predators Stability and global Hopf bifurcation in a delayed food web consisting of a prey and two predators](/preview/png/755955.png)
This paper is concerned with a predator–prey system with Holling II functional response and hunting delay and gestation. By regarding the sum of delays as the bifurcation parameter, the local stability of the positive equilibrium and the existence of Hopf bifurcation are investigated. We obtained explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation. Using a global Hopf bifurcation result of Wu [Wu JH. Symmetric functional differential equations and neural networks with memory, Trans Amer Math Soc 1998;350:4799–4838] for functional differential equations, we may show the global existence of the periodic solutions. Finally, several numerical simulations illustrating the theoretical analysis are also given.
► Some explicit formulas to determine the properties of Hopf bifurcation are given.
► The global existence of these bifurcating periodic solutions is obtained.
► Several numerical simulations are illustrated the theoretical analysis.
► Some simulations are also given to check the fact that hunting delays may be different for various predators.
Journal: Communications in Nonlinear Science and Numerical Simulation - Volume 16, Issue 11, November 2011, Pages 4335–4348