Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing
In this paper, the dynamical behaviors of a 2-component coupled diffusive system modeling hair follicle spacing is considered. For the corresponding ODEs, we not only consider the stability and instability of the unique positive equilibrium solutions, but also show the existence of unstable Hopf bif...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-02-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2023099?viewType=HTML |
| _version_ | 1797833178934673408 |
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| author | Zhili Zhang Aying Wan Hongyan Lin |
| author_facet | Zhili Zhang Aying Wan Hongyan Lin |
| author_sort | Zhili Zhang |
| collection | DOAJ |
| description | In this paper, the dynamical behaviors of a 2-component coupled diffusive system modeling hair follicle spacing is considered. For the corresponding ODEs, we not only consider the stability and instability of the unique positive equilibrium solutions, but also show the existence of unstable Hopf bifurcating periodic solutions. For the reaction-diffusion equations, we are mainly interested in the Turing instability of the positive equilibrium solution, as well as Hopf bifurcations and steady-state bifurcations. Our results showed that, under certain conditions, the reaction-diffusion system not only has Hopf bifurcating periodic solutions (both spatially homogeneous and non-homogeneous, all unstable), but it also has non-constant positive bifurcating equilibrium solutions. This allows for a clearer understanding of the mechanism for the spatiotemporal patterns of this particular system. |
| first_indexed | 2024-04-09T14:19:15Z |
| format | Article |
| id | doaj.art-24c8a075a43d45c5b16f3b15bed7ba4a |
| institution | Directory Open Access Journal |
| issn | 2688-1594 |
| language | English |
| last_indexed | 2024-04-09T14:19:15Z |
| publishDate | 2023-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj.art-24c8a075a43d45c5b16f3b15bed7ba4a2023-05-05T01:18:25ZengAIMS PressElectronic Research Archive2688-15942023-02-013141922194710.3934/era.2023099Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacingZhili Zhang0Aying Wan1Hongyan Lin21. School of Mathematics and Statistics, Hulunbuir University, Hailar, Inner Mongolia 021008, China2. Department of Science and Technology, Hulunbuir University, Hailar, Inner Mongolia 021008, China1. School of Mathematics and Statistics, Hulunbuir University, Hailar, Inner Mongolia 021008, ChinaIn this paper, the dynamical behaviors of a 2-component coupled diffusive system modeling hair follicle spacing is considered. For the corresponding ODEs, we not only consider the stability and instability of the unique positive equilibrium solutions, but also show the existence of unstable Hopf bifurcating periodic solutions. For the reaction-diffusion equations, we are mainly interested in the Turing instability of the positive equilibrium solution, as well as Hopf bifurcations and steady-state bifurcations. Our results showed that, under certain conditions, the reaction-diffusion system not only has Hopf bifurcating periodic solutions (both spatially homogeneous and non-homogeneous, all unstable), but it also has non-constant positive bifurcating equilibrium solutions. This allows for a clearer understanding of the mechanism for the spatiotemporal patterns of this particular system.https://www.aimspress.com/article/doi/10.3934/era.2023099?viewType=HTMLreaction-diffusion modelhopf bifurcationsteady-state bifurcationturing instability |
| spellingShingle | Zhili Zhang Aying Wan Hongyan Lin Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing Electronic Research Archive reaction-diffusion model hopf bifurcation steady-state bifurcation turing instability |
| title | Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing |
| title_full | Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing |
| title_fullStr | Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing |
| title_full_unstemmed | Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing |
| title_short | Spatiotemporal patterns and multiple bifurcations of a reaction- diffusion model for hair follicle spacing |
| title_sort | spatiotemporal patterns and multiple bifurcations of a reaction diffusion model for hair follicle spacing |
| topic | reaction-diffusion model hopf bifurcation steady-state bifurcation turing instability |
| url | https://www.aimspress.com/article/doi/10.3934/era.2023099?viewType=HTML |
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