Turing patterns in nonlinear optics

Nonlinear effects on Turing patterns: time oscillations and chaos.

We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence, the patterns oscillate in time. When varying a single parameter, a series of bifurcations leads to period doubling, quasiperiodic, and chaotic...

Turing Patterns in Deserts

Self-organised patterns of vegetation are a characteristic feature of many semi-arid regions. In particular, banded vegetation is typical on hillsides. Mathematical modelling is widely used to study these banded patterns, because there are no laboratory replicates. I will describe the development of spatial patterns in an established model for banded vegetation via a Turing bifurcation. I will ...

Nonlinear Optics Basics: Kramers-Krönig Relations in Nonlinear Optics

Colour Patterns: Channelling Turing

Very little is known about how animal colour patterns develop. The stripes of the zebrafish provide a tractable a model for colour pattern formation, which now suggests an unconventional patterning mechanism.

Fluctuation-driven Turing patterns.

Models of diffusion-driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of scales in the diffusivities of the constituents of the system in order to predict the formation of spatial patterns. In the context of a very generic model of ...