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... Show moreOne 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. Show less
In the thesis, `Patterns in natural systems’ the formation and evolution of patterns as solutions of several partial differential systems are studied. These mathematical systems model three... Show more In the thesis, `Patterns in natural systems’ the formation and evolution of patterns as solutions of several partial differential systems are studied. These mathematical systems model three different biological and ecological processes. First, the way that plankton concentrates in the water column, under the influence of light and nutrient availability. Second, how tumor cells invade their healthy surroundings when it is incorporated that tumor cells cannot survive in a very small concentration. Lastly, the phenomenon that vegetation in semi-deserts organizes in strikingly regular patterns is studied. The mathematical tools that are used in this thesis, mostly arise from asymptotic analysis and geometric singular perturbation theory. Show less