Wavelength selection beyond turing

Yuval R. Zelnik, Omer Tzuk

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from periodic 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, meaning that many different patterns with different wavelengths are possible for the same set of parameters. Nevertheless, 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 on the phenomena of localized states and repeated local disturbances.

Original languageEnglish
Pages (from-to)2171-2184
Number of pages14
JournalEuropean Physical Journal: Special Topics
Issue number9
StatePublished - 1 Jun 2017

ASJC Scopus subject areas

  • General Materials Science
  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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