Journal of Mathematical Biology

, Volume 69, Issue 6–7, pp 1585–1608 | Cite as

Stochastic amplification of spatial modes in a system with one diffusing species

  • Laura Cantini
  • Claudia Cianci
  • Duccio FanelliEmail author
  • Emma Massi
  • Luigi Barletti
  • Malbor Asllani


The problem of pattern formation in a generic two species reaction–diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by working in the generalized setting of a stochastic formulation to the inspected problem, spatially organized patterns can develop, seeded by finite size corrections. General conditions are given for the stochastic patterns to occur. The predictions of the theory are tested for a specific case study.


Reaction–diffusion Turing instability Stochatic processes 

Mathematics Subject Classification

35B36 35Q84 60G 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Laura Cantini
    • 1
  • Claudia Cianci
    • 2
  • Duccio Fanelli
    • 3
    Email author
  • Emma Massi
    • 1
  • Luigi Barletti
    • 1
  • Malbor Asllani
    • 3
    • 4
  1. 1.Dipartimento di Matematica e Informatica “U. Dini”University of FlorenceFlorenceItaly
  2. 2.Dipartimento di Sistemi e Informatica and INFNUniversity of FlorenceFlorenceItaly
  3. 3.Dipartimento di Fisica e AstronomiaUniversity of Florence and INFNFlorenceItaly
  4. 4.Dipartimento di Scienza e Alta TecnologiaUniversity of InsubriaComoItaly

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