Open AccessThe spatial dynamics of a zebrafish model with cross-diffusions
Author(s) -
Hongyong Zhao,
Qianjin Zhang,
Linhe Zhu
Publication year - 2017
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2017054
Subject(s) - bifurcation , zebrafish , mathematics , turing , hopf bifurcation , dynamics (music) , statistical physics , computer science , spatial ecology , amplitude , mathematical analysis , physics , ecology , nonlinear system , biology , biochemistry , quantum mechanics , acoustics , gene , programming language
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.