Prof. David Lloyd - Approximate Localised Dihedral Patterns Near a Turing Instability

In this talk, we start with some of Alan Turing’s work post his seminal 1952 paper on the chemical basis of morphogenesis and we lead to though to some modern theories of pattern formation involving spatially localised patches of cellular pattern on the plane embedded in a quiescent steady state. Motivated by an physical experiment involving magnetic fluids, we explain how axisymmetric spots can emerge from a pattern forming/Turing instability and then present some recently submitted work on the analysis of emergence of approximate localised cellular patches with dihedral pattern that combines techniques of spatial dynamics for non-autonomous systems and rigorous numerics. Finally, I talk about how we extend these ideas to 3D localised clusters of patterns. This is joint work with Jason Bramburger, Dan Hill and Matt Turner.