The Local Bifurcation and Stability of Nontrivial Steady States of a Logistic Type of Chemotaxis

Chemotaxis is a type of oriented movement of cells in response to the concentration gradient of chemical substances in their environment. We consider local existence and stability of nontrivial steady states of a logistic type of chemotaxis. We carry out the bifurcation theory to obtain the local ex...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2017-07, Vol.33 (3), p.799-808
Main Authors: Cai, Chen-qing, Xu, Qian, Liu, Xiao-lin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Bifurcation theory
Concentration gradient
logistic
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Stability
Steady state
Theoretical
定向运动
定态
局部分岔
局部存在性
浓度梯度
稳定性
趋化性
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Summary:Chemotaxis is a type of oriented movement of cells in response to the concentration gradient of chemical substances in their environment. We consider local existence and stability of nontrivial steady states of a logistic type of chemotaxis. We carry out the bifurcation theory to obtain the local existence of the steady state and apply the expansion method on the chemotaxis to investigate the bifurcation direction. Moreover, by applying the bifurcation direction, we obtain the bifurcating steady state is stable when the bifurcation curve turns to right under certain conditions.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-016-0500-1