Nonlinear systems, patterns and morphogenesis

Nonlinear systems share the universal feature of presenting spontaneous symmetry breaking, typically leading to the formation of regular spatial patterns that are robust and complicated. These patterns may provide the spatial information required by the cells in the process of differentiation and morphogenesis. I will review general properties of nonlinear systems and the basic techniques to study their properties close to bifurcation points. I will present two examples of different problems from physics and their implications in the study of the development of the shape in biology.