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arXiv · 2411.07255

Pattern formation and global analysis of a systematically reduced plant model in dryland environment

Yonghui Xia·Jianglong Xiao·Jianshe Yu
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Abstract

This paper delves into a systematically reduced plant system proposed by Ja\"ibi 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.

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Yonghui Xia, Jianglong Xiao, Jianshe Yu. 2024-10-30. Pattern formation and global analysis of a systematically reduced plant model in dryland environment. https://arxiv.org/abs/2411.07255

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