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

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