Geometry of vegetation patterns: understanding patterns in dryland ecosystems and beyond

Jaïbi, O.

Persistent URL of this record https://hdl.handle.net/1887/3243448

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Jaïbi, O. (2021)

Geometry of vegetation patterns: understanding patterns in dryland ecosystems and beyond

Doctoral Thesis

One of the effects of climate change is the phenomenon of desertification, a process that occurs in semi-arid and arid areas and causes land degradation as well as vegetation loss. Due to the lack of resources, vegetation self-organizes to sustain itself by forming large-scale spatial patterns. In this thesis, the underlying mathematical structure of these observed vegetation patterns is studied using partial differential equations models. The vegetation patterns are analyzed using techniques from geometrical singular perturbation theory and numerical simulations. Additionally, novel multi-front patterns are constructed that arise within one of the models studied. This interdisciplinary research allows for cross-fertilization of both mathematics and ecology.

Desertification

Pattern formation

Dynamical systems

Reaction advection diffusion

Partial differential equations

Multistability

Geometric singular perturbation theory

Ecosystem resilience