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

The Local Bifurcation and Stability of Nontrivial Steady States of a Logistic Type of Chemotaxis
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摘要 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. 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.
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第3期799-808,共10页 应用数学学报(英文版)
基金 supported by the National Natural Science Foundation of China(No.11501031,11471221,71373023) Beijing Natural Science Foundation(1132003 and KZ201310028030) Zhejiang A&F University telant program(2013FR078)
关键词 local bifurcation steady states STABILITY local bifurcation steady states stability
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