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The spatial dynamics of a zebrafish model with cross-diffusions

Hongyong Zhao Qianjin Zhang Linhe Zhu

*Corresponding author: Hongyong Zhao hongyongz@126.com


This paper investigates the spatial dynamics of a zebrafish model with cross-diffusions. Sufficient conditions for Hopf bifurcation and Turing bifurcation are obtained by analyzing the associated characteristic equation. In addition, we deduce amplitude equations based on multiple-scale analysis, and further by analyzing amplitude equations five categories of Turing patterns are gained. Finally, numerical simulation results are presented to validate the theoretical analysis. Furthermore, some examples demonstrate that cross-diffusions have an effect on the selection of patterns, which explains the diversity of zebrafish pattern very well.

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Article URL   http://www.aimspress.com/MBE/article/2181.html
Article ID   1551-0018_2017_4_1035
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