Patterns in natural systems

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. Analysis and Stochastic