Abstract
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.
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