Organizers of this minisymposium are
The formation of patterns or localized structures from a homogeneous rest state is observed frequently in dynamical processes within various scientific disciplines, including chemistry, biology and ecology. Therefore, its mathematical modeling using partial differential equations has attracted much interest. It is well-known that a loss of stability of the homogeneous rest state triggers the formation of periodic structures. However, patterns can also be generated by variance or impurities of system parameters over the domain or in time. Incorporating such spatial and temporal dependence of parameters is a source of new phenomena and challenging mathematics. Besides the question what activates patterns formation, the way in which patterns are generated is also of interest both from a theoretical and applied point of view. They can for instance arise uniformly over the domain, but also in the wake of invading fronts. Finally, the (long-time) dynamical behavior of the generated pattern or localized structure is naturally of importance. In this minisymposium we discuss recent advances in theory of pattern formation and cover some of its applications.