# Wavelength selection beyond Turing

## TL;DR

This paper investigates the selection of spatial pattern wavelengths in natural systems beyond classical Turing instability, focusing on dryland vegetation models and the phenomena of localized states and disturbances.

## Contribution

It explores pattern wavelength selection beyond Turing instability using dryland ecosystem models, highlighting phenomena like localized states and repeated disturbances.

## Key findings

- Wavelength selection can differ significantly beyond Turing instability.
- Localized states influence pattern formation in dryland ecosystems.
- Repeated disturbances impact the emergent spatial patterns.

## Abstract

Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from regular patterns of dryland vegetation to complex structures of bacterial colonies. Many of these patterns can be explained in the context of a Turing instability, where patterns emerge due to two locally interacting components that diffuse with different speeds in the medium. Turing patterns are multistable, such that many different patterns with different wavelengths are possible for the same set of parameters, but in a given region typically only one such wavelength is dominant. In the Turing instability region, random initial conditions will mostly lead to a wavelength that is similar to that of the leading eigenvector that arises from the linear stability analysis, but when venturing beyond, little is known about the pattern that will emerge. Using dryland vegetation as a case study, we use different models of drylands ecosystems to study the wavelength pattern that is selected in various scenarios beyond the Turing instability region, focusing the phenomena of localized states and repeated local disturbances.