Stability and Hopf Bifurcation Analysis in a Delayed Gause-type Predator-prey Models
Authors
Shuang Guo, Xing Qiao, Dongxia Zhao, Lianguang Jia, Xiuyan Jiang
Corresponding Author
Shuang Guo
Available Online May 2018.
- DOI
- 10.2991/ammsa-18.2018.42How to use a DOI?
- Keywords
- gause-type model; stability; hopf bifurcation
- Abstract
A class of delayed ratio-dependent Gause-type predator-prey model is considered. Firstly, the eigenvalue problem is studyed for the linearized system at the coexisting equilibrium and a group of sufficient conditions for the existence of Hopf bifurcation are obtained. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solutions are determined by applying the normal form method and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the obtained results.
- Copyright
- © 2018, the Authors. Published by Atlantis Press.
- Open Access
- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - CONF AU - Shuang Guo AU - Xing Qiao AU - Dongxia Zhao AU - Lianguang Jia AU - Xiuyan Jiang PY - 2018/05 DA - 2018/05 TI - Stability and Hopf Bifurcation Analysis in a Delayed Gause-type Predator-prey Models BT - Proceedings of the 2018 2nd International Conference on Applied Mathematics, Modelling and Statistics Application (AMMSA 2018) PB - Atlantis Press SP - 206 EP - 210 SN - 1951-6851 UR - https://doi.org/10.2991/ammsa-18.2018.42 DO - 10.2991/ammsa-18.2018.42 ID - Guo2018/05 ER -