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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.06681 |
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| _version_ | 1866912845028917248 |
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| author | Tadej, Maciej Martinez-Garcia, Ricardo Hecht, Michael |
| author_facet | Tadej, Maciej Martinez-Garcia, Ricardo Hecht, Michael |
| contents | This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system and provide a rigorous analysis of the conditions required for vegetation survival. Our results identify a critical patch size governed by the trade-off between local growth and boundary losses; habitats smaller than this threshold lead to inevitable extinction. Furthermore, we derive a critical maximal biomass density below which the population collapses to a desert state, regardless of the domain size. We determine stability criteria for stationary solutions and describe the emergence of stable, non-trivial biomass distributions. Numerical experiments comparing sub-Gaussian and super-Gaussian kernels confirm that non-local dispersal mechanisms, particularly those with fat tails, enhance ecosystem resilience by allowing vegetation to persist in smaller, fragmented habitats than predicted by classical local diffusion models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06681 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Extinction and persistence criteria in non-local Klausmeier model of vegetation dynamics on flat landscapes Tadej, Maciej Martinez-Garcia, Ricardo Hecht, Michael Analysis of PDEs This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system and provide a rigorous analysis of the conditions required for vegetation survival. Our results identify a critical patch size governed by the trade-off between local growth and boundary losses; habitats smaller than this threshold lead to inevitable extinction. Furthermore, we derive a critical maximal biomass density below which the population collapses to a desert state, regardless of the domain size. We determine stability criteria for stationary solutions and describe the emergence of stable, non-trivial biomass distributions. Numerical experiments comparing sub-Gaussian and super-Gaussian kernels confirm that non-local dispersal mechanisms, particularly those with fat tails, enhance ecosystem resilience by allowing vegetation to persist in smaller, fragmented habitats than predicted by classical local diffusion models. |
| title | Extinction and persistence criteria in non-local Klausmeier model of vegetation dynamics on flat landscapes |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.06681 |