The spatial dynamics of a zebrafish model with cross-diffusions
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, an...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017054 |
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| _version_ | 1832590047754321920 |
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| author | Hongyong Zhao Qianjin Zhang Linhe Zhu |
| author_facet | Hongyong Zhao Qianjin Zhang Linhe Zhu |
| author_sort | Hongyong Zhao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-594dce09ca4a4f5ea82548212b189772 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-594dce09ca4a4f5ea82548212b1897722025-01-24T02:39:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-07-011441035105410.3934/mbe.2017054The spatial dynamics of a zebrafish model with cross-diffusionsHongyong Zhao0Qianjin Zhang1Linhe Zhu2Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaDepartment of Mathematics, Nanjing University of Aeronautics and Astronautics, School of Mathematical and Natural Sciences, Arizona State University, Nanjing 210016, ChinaThis 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.https://www.aimspress.com/article/doi/10.3934/mbe.2017054cross-diffusionshopf bifurcationturing bifurcationpattern selectionamplitude equationzebrafish |
| spellingShingle | Hongyong Zhao Qianjin Zhang Linhe Zhu The spatial dynamics of a zebrafish model with cross-diffusions Mathematical Biosciences and Engineering cross-diffusions hopf bifurcation turing bifurcation pattern selection amplitude equation zebrafish |
| title | The spatial dynamics of a zebrafish model with cross-diffusions |
| title_full | The spatial dynamics of a zebrafish model with cross-diffusions |
| title_fullStr | The spatial dynamics of a zebrafish model with cross-diffusions |
| title_full_unstemmed | The spatial dynamics of a zebrafish model with cross-diffusions |
| title_short | The spatial dynamics of a zebrafish model with cross-diffusions |
| title_sort | spatial dynamics of a zebrafish model with cross diffusions |
| topic | cross-diffusions hopf bifurcation turing bifurcation pattern selection amplitude equation zebrafish |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017054 |
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