Existence and stability of bifurcating solution of a chemotaxis model

Chen, Mengxin; Srivastava, Hari

doi:10.1090/proc/16536

Existence and stability of bifurcating solution of a chemotaxis model
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by Mengxin Chen and Hari Mohan Srivastava

Proc. Amer. Math. Soc. 151 (2023), 4735-4749

DOI: https://doi.org/10.1090/proc/16536

Published electronically: July 28, 2023

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Abstract:

This paper focuses on a chemotaxis model with no-flux boundary conditions. We first discuss the stability of the unique positive equilibrium by treating the chemotaxis coefficient $\xi$ as the Hopf bifurcation and the steady state bifurcation parameter. Hereafter, we perform the existence and stability of the bifurcating solution, which bifurcated from the steady state bifurcation, by using the Crandall-Rabinowitz local bifurcation theory. It is noticed that few existing literatures give a discriminant to determine the stability of the bifurcating solution for the chemotaxis models. To this end, we will fill this gap, and an explicit formula will be presented. This technique can also be applied in other ecological models with chemotaxis.

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