QUALITATIVE ANALYSIS ON POSITIVE STEADY-STATES FOR AN AUTOCATALYTIC REACTION MODEL IN THERMODYNAMICS

被引：16

作者：

Jia, Yunfeng ^{[1
]}

Li, Yi ^{[2
]}

Wu, Jianhua ^{[1
]}

机构：

[1] Shaanxi Normal Univ, Sch Math & Informat Sci, Xian 710062, Shaanxi, Peoples R China

[2] Calif State Univ Northridge, Dept Math, Northridge, CA 91325 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 09期

关键词：

Autocatalytic reaction model; positive steady-state; stability; existence and non-existence; bifurcation; numerical simulation; STIRRED-TANK REACTOR; DIFFUSION; INSTABILITIES; BIFURCATION; SYSTEM; BOUNDS;

D O I：

10.3934/dcds.2017206

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a reaction-diffusion system known as an autocatalytic reaction model is considered. The model is characterized by a system of two differential equations which describe a type of complex biochemical reaction. Firstly, some basic characterizations of steady-state solutions of the model are presented. And then, the stability of positive constant steady-state solution and the non-existence, existence of non-constant positive steady-state solutions are discussed. Meanwhile, the bifurcation solution which emanates from positive constant steady-state is investigated, and the global analysis to the system is given in one dimensional case. Finally, a few numerical examples are provided to illustrate some corresponding analytic results.

引用

页码：4785 / 4813

页数：29

共 50 条

[41] REACTION NETWORK STRUCTURE AND MULTIPLE STEADY-STATES IN COMPLEX ISOTHERMAL REACTORS
FEINBERG, M
ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, 1985, 189 (APR-): : 35 - INDE
[42] MULTIPLE STEADY-STATES IN REACTION CONTROLLED SURFACE CATALYZED-REACTIONS
TAKOUDIS, CG
SCHMIDT, LD
ARIS, R
CHEMICAL ENGINEERING SCIENCE, 1981, 36 (02) : 377 - 386
[43] EXPERIMENTAL STABILIZATION OF UNSTABLE STEADY-STATES IN OSCILLATORY AND EXCITABLE REACTION SYSTEMS
HJELMFELT, A
ROSS, J
JOURNAL OF PHYSICAL CHEMISTRY, 1994, 98 (04): : 1176 - 1179
[44] Unstable and stable steady-states in the Kiyotaki-Wright model
Juan-Manuel Renero
Economic Theory, 1998, 11 : 275 - 294
[45] Stability analysis on steady-state bifurcation for arbitrary order autocatalytic reaction model
Zhao, Jiantang
Jia, Yunfeng
APPLIED MATHEMATICS LETTERS, 2019, 95 : 98 - 103
[46] ON THE STABILITY AND INSTABILITY OF POSITIVE STEADY-STATES OF A SEMILINEAR HEAT-EQUATION IN RN
GUI, CF
NI, WM
WANG, XF
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1992, 45 (09) : 1153 - 1181
[47] The Existence of Positive Nonconstant Steady States in a Reaction: Diffusion Epidemic Model
Yuan, Yuan
Wang, Hailing
Wang, Weiming
ABSTRACT AND APPLIED ANALYSIS, 2013,
[48] ANALYSIS OF FLUCTUATIONS IN CHEMICAL-REACTIONS WITH SEVERAL STEADY-STATES
GRECHANNIKOV, AV
YABLONSKII, GS
REACTION KINETICS AND CATALYSIS LETTERS, 1982, 19 (3-4): : 321 - 325
[49] The Qualitative Analysis of a Class Autocatalytic Reactions Model
沈伯骞
张成
数学季刊, 1999, (02) : 11 - 20
[50] THE STABILITY OF STEADY-STATES IN A ONE-DIMENSIONAL MODEL OF STANDPIPE FLOW
RANGACHARI, S
JACKSON, R
POWDER TECHNOLOGY, 1982, 31 (02) : 185 - 196

← 1 2 3 4 5 →