Stability analysis of a chemostat model with maintenance energy

被引：79

作者：

Zhang, Tonghua ^{[1
]}

Zhang, Tongqian ^{[2
,3
]}

Meng, Xinzhu ^{[2
,3
]}

机构：

[1] Swinburne Univ Technol, Dept Math, Melbourne, Vic 3122, Australia

[2] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Peoples R China

[3] Shandong Univ Sci & Technol, State Key Lab Min Diaster Prevent & Control, Co Founded Shandong Prov & Minist Sci & Technol, Qingdao 266590, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2017年 / 68卷

基金：

中国国家自然科学基金;

关键词：

Diffusion; Global stability; Local stability; Membrane reactor; REACTION-DIFFUSION SYSTEM; GLOBAL STABILITY; REACTOR; BIOLOGY;

D O I：

10.1016/j.aml.2016.12.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we dedicate ourselves to the study of a diffusive model for unstirred membrane reactors with maintenance energy and subject to a homogeneous Neumann boundary condition. It shows that the unique constant steady state is globally asymptotically stable when it exists. This result further implies the nonexistence of any spatial patterns. (C) 2016 Elsevier Ltd. All rights reserved.

引用

页码：1 / 7

页数：7

共 17 条

[1]

[Anonymous], 2002, Mathematical biology, Interdisciplinary applied mathematics

[2]

[Anonymous], 1993, LECT NOTES MATH

[3] Long time behaviour of a stochastic model for continuous flow bioreactor [J].

Chen, Zhenzhen ;

Zhang, Tonghua .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2013, 51 (02) :451-464

[4] Global stability for reaction-diffusion equations in biology [J].

Hattaf, Khalid ;

Yousfi, Noura .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (08) :1488-1497

[5] A survey of constructing Lyapunov functions for mathematical models in population biology [J].

Hsu, SB .

TAIWANESE JOURNAL OF MATHEMATICS, 2005, 9 (02) :151-173

[6] FURTHER STUDIES OF A REACTION-DIFFUSION SYSTEM FOR AN UNSTIRRED CHEMOSTAT WITH INTERNAL STORAGE [J].

Hsu, Sze-Bi ;

Shi, Junping ;

Wang, Feng-Bin .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, 19 (10) :3169-3189

[7] On a system of reaction-diffusion equations arising from competition with internal storage in an unstirred chemostat [J].

Hsu, Sze-Bi ;

Jiang, Jifa ;

Wang, Feng-Bin .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 248 (10) :2470-2496

[8] Wave-induced chaos in a continuously fed unstirred reactor [J].

Merkin, JH ;

Petrov, V ;

Scott, SK ;

Showalter, K .

JOURNAL OF THE CHEMICAL SOCIETY-FARADAY TRANSACTIONS, 1996, 92 (16) :2911-2918

[9] A fundamental analysis of continuous flow bioreactor and membrane reactor models with death and maintenance included [J].

Nelson, Mark Ian ;

Kerr, Tara Bridget ;

Chen, Xiao Dong .

ASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, 2008, 3 (01) :70-80

[10] Global stability of the equilibrium of a diffusive Holling-Tanner prey-predator model [J].

Peng, Rui ;

Wang, Mingxin .

APPLIED MATHEMATICS LETTERS, 2007, 20 (06) :664-670

← 1 2 →