You Position: Home > Paper
Stability and Hopf Bifurcation Analysis of a Delayed Predator-Prey Model with Constant Rate Harvesting
( views:17, downloads:0 )
- Author:
- No author available
- Journal Title:
- JOURNAL OF BIOMATHEMATICS
- Issue:
- 4
- DOI:
- No doi available
- Key Word:
- 捕食系统;时滞;Hopf分支;Predator-prey model;Time delay;Hopf Bifurcation
Abstract： In this paper, by using the method of qualitative analysis, we investigate the effect of time delay on the dynamics of a predator-prey model with constant rate harvesting to prey. We obtain the conditions of local stability and the occurrence of Hopf bifurcation. Furthermore, we present a theoretical analysis of the direction and stability of the Hopf bifurcation. And two examples which give numerical simulation results are performed to support the theoretical predictions.
- [1]段文英.关于具时滞的捕食-被捕食系统的稳定性与Hopf分支[J].2004,(1).
- [2]李林.一个时滞微分系统的稳定性与Hopf分支[J].2002,(2).
- [3]唐长兵,管俊彪,沈绍伟.一类三阶时滞微分系统的稳定性与Hopf分支研究[J].2007,(4).
- [4]XIANZHANG MENG,YONGLI SONG,DONG HAN.Stability and Bifurcation in a Non-Kolmogorov Type Prey-Predator System with Time Delay[J].2005,41(13).
- [5]G. Pecelli.Prey-predator systems with delay: Hopf bifurcation and stable oscillations[J].1997,25(10).
- [6]Chen YY,Song CM.Stability and Hopf bifurcation analysis in a prey-predator system with stage-structure for prey and time delay[J].2008,38(4).
- [7]Yan XP,Zhang CH.Hopf bifurcation in a delayed Lokta-Volterra predator-prey system[J].2008,9(1).
- [8]Han MA,Lin YP,Chen YY,etc.Global qualitative analysis for a predator-prey system with delay[J].2007,32(4).
- [9]Li WT,Yan XP.Hopf bifurcation and global periodic solutions in a delayed predator-prey system[J].2006,177(1).
- [10]Liu ZH,Yuan R.Stability and bifurcation in a harvested one-predator-two-prey model with delays[J].2006,27(5).
- [11]Wei JJ,Song YL.Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system[J].2005,301(1).
- [12]Xu R,Ma Z.Stability and Hopf bifurcation in a predator-prey model with stage structure for the predator[J].2008,9(4).
- [13]Yahong Peng,Yongli Song,Junjie Wei.Bifurcations for a predator-prey system with two delays[J].2008,337(1).
- [14]T. Faria,L.T. Magalhaes.Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation[J].1995,122(2).