BIFURCATIONS WITH MULTI-DIMENSIONAL KERNEL IN A CHEMOTAXIS-GROWTH SYSTEM

Taka-aki Aoki; Koichi Osaki

doi:10.32219/isms.82.2_155

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Keywords: chemotaxis-growth system, Lyapunov-Schmidt reduction, bifurcation, codimension-two bifurcation, codimension-three bifurcation

JOURNAL FREE ACCESS

2019 Volume 82 Issue 2 Pages 155-169

DOI https://doi.org/10.32219/isms.82.2_155

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Abstract

We study the bifurcation problem for a chemotaxis-growth system with logistic growth in a two-dimensional rectangular domain. We apply the local bifurcation theorem by Ambrosetti and Prodi that does not require one-dimensional degeneration of the linearized operator around trivial solutions. We then obtain bifurcation solutions with two- and three-dimensional degeneration indicating spatially regular nesting patterns.

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