Lines in the sand : behaviour of self-organised vegetation patterns in dryland ecosystems

Bastiaansen, R. (2019)

Doctoral Thesis

Vast, often populated, areas in dryland ecosystems face the dangers of desertification. Loosely speaking, desertification is the process in which a relatively dry region loses its vegetation - typically as an effect of climate change. As an important step in this process, the lack of resources forces the vegetation in these semi-arid areas to organise itself into large-scale spatial patterns. In this thesis, these patterns are studied using conceptual mathematical models, in which vegetation patterns present themselves as localised structures (for example pulses or fronts). These are analysed using mathematical techniques from (geometric singular) perturbation theory and via numerous numerical simulations. The study of these ecosystem models leads to new advances in both mathematics and ecology.

• Desertification
• Pattern formation
• Reaction advection diffusion
• Multistability
• Semi-strong pulse dynamics
• Asymptotic analysis
• Geometric singular perturbations
• Exponential dichotomies
• Changing parameters
• Ecosystem resilience

• All authors: Bastiaansen, R.
• Supervisor: Doelman, A.; Rietkerk, M.
• Co-supervisor: Chirilus-Bruckner, M.
• Committee: Vaart, A. van der; Merks, R.; Eppinga, M.; Rademacher, J.; Silber, M.
• Qualification: Doctor (dr.)
• Awarding Institution: Mathematical Institute, Faculty of Science, Leiden University
• Date: 2019-06-27
• Sponsorship: NWO Mathematics of Planet Earth