Abstract of the talk// Maciej discusses ongoing research on a non-local Klausmeier model for vegetation dynamics in drylands, developed in collaboration with Dr. Ricardo Martínez-García. The model captures interactions between plant density and water availability in finite domains through integro-differential equations with non-local dispersal kernels. Unlike classical approaches, which often assume artificial periodic boundary conditions or infinite spatial domains to simplify mathematical analysis, this work focuses on bounded regions that more accurately reflect realistic ecological settings. Current efforts aim to investigate the mathematical properties of the model, such as well-posedness and stability conditions, while also exploring numerical methods to simulate vegetation patterns.
Understanding vegetation dynamics in drylands is crucial, as these regions cover a significant portion of Earth’s surface and are home to vulnerable populations. By introducing more realistic descriptions of spatial interactions and desertification processes, this research addresses key gaps in existing ecological models, which often neglect critical drivers of vegetation loss. The insights gained from this work have the potential to improve predictions of dryland ecosystem responses to environmental changes and inform strategies to mitigate the impacts of desertification.