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Affiliation of Author(s):理学院

Title of Paper:THE SPATIAL DYNAMICS OF A ZEBRAFISH MODEL WITH CROSS-DIFFUSIONS

Journal:MATHEMATICAL BIOSCIENCES AND ENGINEERING

Key Words:Cross-diffusions Hopf bifurcation turing bifurcation pattern selection amplitude equation zebrafish

Abstract: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.

ISSN No.:1547-1063

Translation or Not:no

Date of Publication:2017-08-01

Co-author:Zhang, Qianjin,Zhu, Linhe

Correspondence Author:zhy