• Previous Article
    Asymptotic properties of a delayed SIR epidemic model with density dependent birth rate
  • DCDS-B Home
  • This Issue
  • Next Article
    Persistence and periodic solutions of a nonautonomous predator-prey diffusion with Holling III functional response and continuous delay
August  2004, 4(3): 663-670. doi: 10.3934/dcdsb.2004.4.663

Global stability for a chemostat-type model with delayed nutrient recycling

1. 

Department of Mathematics, Henan Normal University, Xin Xiang, 453002, China

Received  December 2002 Revised  January 2004 Published  May 2004

In this paper, we consider the question of global stability of the positive equilibrium in a chemostat-type system with delayed nutrient recycling. By constructing Liapunov function, we obtain a sufficient condition for the global stability of the positive equilibrium.
Citation: Zhiqi Lu. Global stability for a chemostat-type model with delayed nutrient recycling. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 663-670. doi: 10.3934/dcdsb.2004.4.663
[1]

Hua Nie, Feng-Bin Wang. Competition for one nutrient with recycling and allelopathy in an unstirred chemostat. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2129-2155. doi: 10.3934/dcdsb.2015.20.2129

[2]

Saroj Panigrahi. Liapunov-type integral inequalities for higher order dynamic equations on time scales. Conference Publications, 2013, 2013 (special) : 629-641. doi: 10.3934/proc.2013.2013.629

[3]

Ahuod Alsheri, Ebraheem O. Alzahrani, Asim Asiri, Mohamed M. El-Dessoky, Yang Kuang. Tumor growth dynamics with nutrient limitation and cell proliferation time delay. Discrete and Continuous Dynamical Systems - B, 2017, 22 (10) : 3771-3782. doi: 10.3934/dcdsb.2017189

[4]

Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, 2021, 29 (4) : 2599-2618. doi: 10.3934/era.2021003

[5]

Linfeng Mei, Feng-Bin Wang. Dynamics of phytoplankton species competition for light and nutrient with recycling in a water column. Discrete and Continuous Dynamical Systems - B, 2021, 26 (4) : 2115-2132. doi: 10.3934/dcdsb.2020359

[6]

Alessandro Paolucci, Cristina Pignotti. Well-posedness and stability for semilinear wave-type equations with time delay. Discrete and Continuous Dynamical Systems - S, 2022, 15 (6) : 1561-1571. doi: 10.3934/dcdss.2022049

[7]

Brittni Hall, Xiaoying Han, Peter E. Kloeden, Hans-Werner van Wyk. A nonautonomous chemostat model for the growth of gut microbiome with varying nutrient. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022075

[8]

Songbai Guo, Wanbiao Ma. Global dynamics of a microorganism flocculation model with time delay. Communications on Pure and Applied Analysis, 2017, 16 (5) : 1883-1891. doi: 10.3934/cpaa.2017091

[9]

Cruz Vargas-De-León, Alberto d'Onofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1019-1033. doi: 10.3934/mbe.2017053

[10]

Frédéric Mazenc, Michael Malisoff, Patrick D. Leenheer. On the stability of periodic solutions in the perturbed chemostat. Mathematical Biosciences & Engineering, 2007, 4 (2) : 319-338. doi: 10.3934/mbe.2007.4.319

[11]

Mary Ballyk, Ross Staffeldt, Ibrahim Jawarneh. A nutrient-prey-predator model: Stability and bifurcations. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 2975-3004. doi: 10.3934/dcdss.2020192

[12]

C. Connell McCluskey. Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence. Mathematical Biosciences & Engineering, 2010, 7 (4) : 837-850. doi: 10.3934/mbe.2010.7.837

[13]

C. Connell McCluskey. Global stability for an SEIR epidemiological model with varying infectivity and infinite delay. Mathematical Biosciences & Engineering, 2009, 6 (3) : 603-610. doi: 10.3934/mbe.2009.6.603

[14]

Bao-Zhu Guo, Li-Ming Cai. A note for the global stability of a delay differential equation of hepatitis B virus infection. Mathematical Biosciences & Engineering, 2011, 8 (3) : 689-694. doi: 10.3934/mbe.2011.8.689

[15]

Anatoli F. Ivanov, Musa A. Mammadov. Global asymptotic stability in a class of nonlinear differential delay equations. Conference Publications, 2011, 2011 (Special) : 727-736. doi: 10.3934/proc.2011.2011.727

[16]

Yincui Yan, Wendi Wang. Global stability of a five-dimensional model with immune responses and delay. Discrete and Continuous Dynamical Systems - B, 2012, 17 (1) : 401-416. doi: 10.3934/dcdsb.2012.17.401

[17]

Gongwei Liu, Baowei Feng, Xinguang Yang. Longtime dynamics for a type of suspension bridge equation with past history and time delay. Communications on Pure and Applied Analysis, 2020, 19 (10) : 4995-5013. doi: 10.3934/cpaa.2020224

[18]

Serge Nicaise, Cristina Pignotti, Julie Valein. Exponential stability of the wave equation with boundary time-varying delay. Discrete and Continuous Dynamical Systems - S, 2011, 4 (3) : 693-722. doi: 10.3934/dcdss.2011.4.693

[19]

Xiang Xie, Honglei Xu, Xinming Cheng, Yilun Yu. Improved results on exponential stability of discrete-time switched delay systems. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 199-208. doi: 10.3934/dcdsb.2017010

[20]

Mohamed Dellal, Bachir Bar. Global analysis of a model of competition in the chemostat with internal inhibitor. Discrete and Continuous Dynamical Systems - B, 2021, 26 (2) : 1129-1148. doi: 10.3934/dcdsb.2020156

2021 Impact Factor: 1.497

Metrics

  • PDF downloads (82)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]