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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.07255 |
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| _version_ | 1866910695064338432 |
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| author | Xia, Yonghui Xiao, Jianglong Yu, Jianshe |
| author_facet | Xia, Yonghui Xiao, Jianglong Yu, Jianshe |
| contents | This paper delves into a systematically reduced plant system proposed by Jaïbi et al. [Phys. D, 2020] in arid area. They used the method of geometric singular perturbation to study the existence of abundant orbits. Instead, we deliberate the stability and distributed patterns of this system. For a non-diffusive scenario for the model, we scrutinize the local and global stability of equilibria and derive conditions for the existence or non-existence of the limit cycle. The bifurcation behaviors are also explored. For the spatial model, we investigate Hopf, Turing, Hopf-Turing, Turing-Turing bifurcations. Specially, the evolution process from periodic solutions to spatially nonconstant steady states is observed near the Hopf-Turing bifurcation point. And mixed nonconstant steady states near the Turing-Turing bifurcation point are observed. Furthermore, it's found that there exist gap, spot, stripe and mixed patterns. The seed-dispersal rate enables the transformation of pattern structures. Reasonable control of system parameters may prevent desertification from occurring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pattern formation and global analysis of a systematically reduced plant model in dryland environment Xia, Yonghui Xiao, Jianglong Yu, Jianshe Pattern Formation and Solitons Dynamical Systems This paper delves into a systematically reduced plant system proposed by Jaïbi et al. [Phys. D, 2020] in arid area. They used the method of geometric singular perturbation to study the existence of abundant orbits. Instead, we deliberate the stability and distributed patterns of this system. For a non-diffusive scenario for the model, we scrutinize the local and global stability of equilibria and derive conditions for the existence or non-existence of the limit cycle. The bifurcation behaviors are also explored. For the spatial model, we investigate Hopf, Turing, Hopf-Turing, Turing-Turing bifurcations. Specially, the evolution process from periodic solutions to spatially nonconstant steady states is observed near the Hopf-Turing bifurcation point. And mixed nonconstant steady states near the Turing-Turing bifurcation point are observed. Furthermore, it's found that there exist gap, spot, stripe and mixed patterns. The seed-dispersal rate enables the transformation of pattern structures. Reasonable control of system parameters may prevent desertification from occurring. |
| title | Pattern formation and global analysis of a systematically reduced plant model in dryland environment |
| topic | Pattern Formation and Solitons Dynamical Systems |
| url | https://arxiv.org/abs/2411.07255 |