Bifurcation and Stability of the Steady-State Solutions to a System with Cross-Difusion Effect

Journal of South China University of Technology (Natural Science Edition) ›› 2005, Vol. 33 ›› Issue (2): 99-102.

Bifurcation and Stability of the Steady-State Solutions to a System with Cross-Difusion Effect

Dai Wan-yi Fu Yi-ping

College of Mathematical Sciences,South China Univ.of Tech.,Guangzhou 510640,Guangdong,China

Received:2004-05-18 Online:2005-02-25 Published:2005-02-25
Contact: 戴婉仪(1971-)，女，在职硕士生，现为华南农业大学理学院讲师，主要从事微分方程与数理金融方面的研究 E-mail:dwy@scut.edu.cn
About author:戴婉仪(1971-)，女，在职硕士生，现为华南农业大学理学院讲师，主要从事微分方程与数理金融方面的研究
Supported by:
国家自然科学基金资助项目(10171032)

Abstract

Abstract:

The aim of this paper is to investigate the bifurcation and stability of the positive steady-state solutions to a mathematical biology model of two competition species. These two species interact with each other under the cross-difusion effect.In this investigation,the spectral analysis method and the bifurcation theory are employed to analyze the stab ility of the semitrivial steady-state solutions.Then,by respectively using the growth rates a and b as bifurcation parameters,the existence and stability of the nontrivial positive steady-state solutions from the semitrivial steady-state solutions are obtained.Th e above-mentioned results are finally applied to a specific biology model,with the conclusion that there are nontrivial positive steady-state solutions when a and b Iie in some specific ranges.The necessary and sufficient conditions for the asymptotical stability of the solutions ale also proved.

Key words: system with cross-difusion effect, steady-state solution, bifurcation, stability

Dai Wan-yi Fu Yi-ping. Bifurcation and Stability of the Steady-State Solutions to a System with Cross-Difusion Effect[J]. Journal of South China University of Technology (Natural Science Edition), 2005, 33(2): 99-102.

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Bifurcation and Stability of the Steady-State Solutions to a System with Cross-Difusion Effect

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