Bogdanov-Takens bifurcation with codimension three of a predator-prey system suffering the additive Allee effect  

作　　者：Yanwei Liu Zengrong Liu Ruiqi Wang 

机构地区：[1]College of MathemaLics and Information Science Zhengzhou University of Light Industry Zhengzhou 450002, P. R. China [2]Department of Mathematics, Shanghai University Shanghai 200444, P. R. China

出　　处：《International Journal of Biomathematics》2017年第3期261-284,共24页生物数学学报（英文版）

基　　金：The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This research is supported by the National Natural Science Foundation of China （No. 11171206）. This research is also sponsored by the Research Fund for the Doctoral Program of Zhengzhou University of Light Industry.

摘　　要：In the present work, research efforts have focused on investigating codimension two and three Bogdanov-Takens bifurcations of a predator-prey system with additive Allee effect. According to the existence conditions of Bogdanov-Takens bifurcation, we give the associated generic unfolding, and derive the dynamical classification in the perturbation parameter plane using some smooth parameter-dependent transformations of coordinate. Moreover, some numerical examples and simulations are performed to complete and illustrate our results.

关 键 词：Bogdanov-Takens bifurcation Allee effect universal unfolding 

分 类 号：G[文化科学]