数学

具有年龄结构的捕食被捕食系统的 Bogdanov-Takens 分支

  • 刘霞 ,
  • 焦建锋
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  • 河南师范大学~~数学与信息科学学院~~大数据统计分析与优化控制河南省工程实验室,河南~~新乡 453007
刘 霞, 女, 副教授, 硕士生导师, 研究方向为生物数学

收稿日期: 2015-06-08

  网络出版日期: 2016-09-22

基金资助

河南省教育厅科学技术研究重点项目(14A110019, 15A110034);
河南师范大学校级骨干教师项目资助

Bogdanov-Takens bifurcation for a delayed predator prey system with stage structure

  • LIU Xia ,
  • JIAO Jian-Feng
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Received date: 2015-06-08

  Online published: 2016-09-22

摘要

本文考虑了一类具有常值收获和年龄结构的捕食被捕食系统的~Bogdanov-Takens(BT)分支问题.给出了系统的正平衡点是BT奇点的充分条件以及系统在该奇点处的开拆标准型,从而得出在该平衡点附近处会出现的分支现象

本文引用格式

刘霞 , 焦建锋 . 具有年龄结构的捕食被捕食系统的 Bogdanov-Takens 分支[J]. 华东师范大学学报(自然科学版), 2016 , 2016(3) : 39 -47 . DOI: 2016.03.005

Abstract

In this paper the Bogdanov-Takens (BT) bifurcation of a delayed predator prey system with stage structure and constant harvesting is considered. The existing conditions which guarantee an interior equilibrium of the system is BT singularity are obtained and the corresponding normal form for the system at this singularity is presented, some bifurcation results are shown

参考文献

[1]XU R. Global stability and Hopf bifurcation of a predator-prey model with stage structure and delayed predator response [J]. Nonlinear Dyn, 2012, 67: 1683-1693.
[2]DENG L W, WANG X D, PENG M. Hopf bifurcation analysis for a ratio-dependent predator-prey system with two delays and stage structure for the predator [J].Applied Mathematics and Computation, 2014, 231: 214-230.
[3]WANG L, FAN Y, LI W. Multiple bifurcations in a predator-prey system with monotonic functional response [J]. Applied Mathematics and Computation, 2006, 172: 1103-1120.
[4]XIAO D M , RUAN S G. Multiple bifurcation in a delayed predator-prey system with nonmonotonic functional response [J]. Journal of Differential Equations, 2001, 176: 494-510.
[5]XIA J, LIU Z, YUAN R, et al. The effects of harvesting and time delay on predator-prey systems with Holling type II functional response [J]. SIAM J Appl Math, 2009, 70: 1178-1200.
[6]JIANG J, SONG Y L. Delay-induced Bogdanov-Takens bifurcation in a Leslie-Gower predator-prey model with nonmonotonic functional response [J].Commun Nonlinear Sci Numer Simulat, 2014, 19: 2454-2465.
[7] CAMPBELL S A, YUAN Y. Zero singularities of codimension two and three in delay differential equations [J].  Nonlinearity, 2008,  21:2671-2691.
[8] GUO S J, MAN J J.  Center manifolds theorem for parameterized delay differential equations with applications to zero singularities [J]. Nonlinear Analysis, 2011, 74: 4418-4432.
[9] QIAO Z Q, LIU X B, ZHU D M. Bifurcation in delay differential systems with triple-zero singularity [J]. Chinese Ann Math Ser A, 2010, 31:59-70.
[10] FARIA T, MAGALH widetilde A ES L T.  Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity [J]. Journal of Differential Equations, 1995, 122:201-224.
[11] CHOW S N, LI C Z, WANG D.  Normal Forms and Bifurcation of Planar Vector Fields [M]. Cambridge: Cambridge University Press, 1994.
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