一类具有自动催化作用和饱和定律的双分子模型的图灵不稳定性和霍普夫分歧

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 366-373.

一类具有自动催化作用和饱和定律的双分子模型的图灵不稳定性和霍普夫分歧

周军

西南大学数学与统计学院重庆 400715

收稿日期:2016-06-14 修回日期:2016-10-18 出版日期:2017-04-26 发布日期:2017-04-26
作者简介:周军,jzhou@swu.edu.cn
基金资助:
国家自然科学基金（11201380）、重庆市基础科学与前沿技术研究专项（cstc2016jcyjA0018）、中国博士后基金（2014M550453，2015T80948）和中央高校基本科研业务费（XDJK2015A16）

Turing Instability and Hopf Bifurcation of a Bimolecular Model with Autocatalysis and Saturation Law

Zhou Jun

School of Mathematics and Statistics, Southwest University, Chongqing 400715

Received:2016-06-14 Revised:2016-10-18 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the NSFC (11201380), the Basic and Advanced Research Project of CQC-STC (cstc2016jcyjA0018), the China Postdoctoral Science Foundation (2014M550453, 2015T80948) and the Fundamental Research Funds for the Central Universities (XDJK2015A16)

摘要/Abstract

摘要： 通过分析线性化系统的特征值并利用分歧定理，研究了一类具有自动催化作用和饱和定律的双分子模型的图灵不稳定性和霍普夫分歧，并利用数值模拟的方法证明和解释了理论结果.

关键词: 双分子模型, 自动催化作用, 图灵不稳定性, 霍普夫分歧

Abstract: This paper deals with a bimolecular model with autocatalysis and saturation law. By analyzing the eigenvalues of the linearized system and using the bifurcation theory, we derive the conditions to occurrence Turing instability and Hopf bifurcation from the unique constant solution. Numerical simulations are presented to verify and illustrate the theoretical results.

Key words: Bimolecular model, Autocatalysis, Turing instability, Hopf bifurcation

中图分类号:

O175.26

周军. 一类具有自动催化作用和饱和定律的双分子模型的图灵不稳定性和霍普夫分歧[J]. 数学物理学报, 2017, 37(2): 366-373.

Zhou Jun. Turing Instability and Hopf Bifurcation of a Bimolecular Model with Autocatalysis and Saturation Law[J]. Acta mathematica scientia,Series A, 2017, 37(2): 366-373.

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