Stability and bifurcation of a simple food chain in a chemostat with removal rates

被引：13
|
作者：
El-Sheikh, MMA [1 ]
Mahrouf, SAA [1 ]
机构：
[1] Menoufia Univ, Fac Sci, Dept Math, Shibin Al Kawm, Egypt
来源：
CHAOS SOLITONS & FRACTALS | 2005年 / 23卷 / 04期
关键词：
D O I：
10.1016/j.chaos.2004.06.079
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we consider a model describing predator-prey interactions in a chemostat that incorporates genreal response functions and distinct removal rates. In this case, the conservation law fails. To overcome this problem, we use Liapunov functions in the study of the global stability of equlibria. Mathematical analysis of the model equations with regard to invariance of non-negativity, boundedness of solutions, dissipativity and persistence are studied. Hopf bifurcation theory is applied. (C) 2004 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1475 / 1489
页数：15
相关论文
共 50 条
  • [1] Simple food chain in a chemostat with distinct removal rates
    Li, BT
    Kuang, Y
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 242 (01) : 75 - 92
  • [2] Bifurcation and chaos of Tessiet type food chain chemostat with periodically varying substrate
    Guoping Pang
    Yanlai Liang
    Fengyan Wang
    Journal of Mathematical Chemistry, 2008, 44 : 674 - 690
  • [3] Bifurcation and chaos in a Tessiet type food chain chemostat with pulsed input and washout
    Wang, Fengyan
    Hao, Chunping
    Chen, Lansun
    CHAOS SOLITONS & FRACTALS, 2007, 32 (04) : 1547 - 1561
  • [4] Bifurcation and chaos in a Monod type food chain chemostat with pulsed input and washout
    Wang, Fengyan
    Hao, Chunping
    Chen, Lansun
    CHAOS SOLITONS & FRACTALS, 2007, 31 (04) : 826 - 839
  • [5] Bifurcation and chaos of Tessiet type food chain chemostat with periodically varying substrate
    Pang, Guoping
    Liang, Yanlai
    Wang, Fengyan
    JOURNAL OF MATHEMATICAL CHEMISTRY, 2008, 44 (03) : 674 - 690
  • [6] Stability and bifurcation of stochastic chemostat model
    Nia, Mehdi Fatehi
    Khajoei, Najmeh
    JOURNAL OF MATHEMATICAL MODELING, 2023, 11 (02): : 375 - 394
  • [7] HOPF BIFURCATION FOR SIMPLE FOOD CHAIN MODEL WITH DELAY
    Cavani, Mario
    Lara, Teodoro
    Romero, Sael
    ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2009,
  • [8] Food chain dynamics in the chemostat
    Boer, MP
    Kooi, BW
    Kooijman, SALM
    MATHEMATICAL BIOSCIENCES, 1998, 150 (01) : 43 - 62
  • [9] STABILITY AND BIFURCATION ANALYSIS OF FILIPPOV FOOD CHAIN SYSTEM WITH FOOD CHAIN CONTROL STRATEGY
    Hamdallah, Soliman A. A.
    Tang, Sanyi
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2020, 25 (05): : 1631 - 1647
  • [10] Stability and Bifurcation Analysis in a Food Chain Model with Delay
    Zhang, Li
    MECHANICAL AND AEROSPACE ENGINEERING, PTS 1-7, 2012, 110-116 : 3382 - 3388
12345