Spatial pattern formation induced by Gaussian white noise

Mathematical Biosciences
Stefania ScarsoglioLuca Ridolfi

Abstract

The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics term, accounting for the local rate of variation of the field variable, (ii) a noise component (additive or multiplicative) accounting for the unavoidable environmental disturbances, and (iii) a linear spatial coupling component, which provides spatial coherence and takes into account diffusion mechanisms. We investigate these dynamics using analytical tools, such as mean-field theory, linear stability analysis and structure function analysis, and use numerical simulations to confirm these analytical results.

References

May 10, 2011·Journal of Theoretical Biology·Vicenç MéndezWerner Horsthemke
Mar 9, 2013·Bulletin of Mathematical Biology·Alan J McKaneTim Rogers
Jun 29, 2016·Journal of Pharmacokinetics and Pharmacodynamics·Krzysztof PuszynskiAlberto d'Onofrio
Sep 22, 2016·Scientific Reports·Ignacio BordeuMustapha Tlidi
Sep 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Thomas E WoolleyPhilip K Maini
Jun 29, 2018·Scientific Reports·Immanuel Meyer, Nadav M Shnerb
Oct 3, 2019·Physical Review. E·Peter H BaxendaleLawrence M Ward

Citations

Dec 19, 1994·Physical Review Letters· Van den Broeck CR Toral
Aug 28, 1995·Physical Review Letters·M WuD S Cannell
Apr 22, 1996·Physical Review Letters·J ArmeroF Sagués
Nov 4, 1996·Physical Review Letters·B J GluckmanS J Schiff
Jun 12, 1999·Science·C A Klausmeier
Nov 3, 2001·Physical Review Letters·Jost von HardenbergY Zarmi
Feb 28, 2002·Physical Review Letters·J W Shuai, P Jung
Aug 1, 2002·Journal of Mathematical Biology·M O'Callaghan, A G Murray
Apr 20, 2004·Physical Review Letters·Amilcare Porporato, Paolo D'Odorico
Sep 28, 2004·Science·Max RietkerkJohan van de Koppel
Jul 27, 2005·Proceedings of the National Academy of Sciences of the United States of America·Paolo D'OdoricoLuca Ridolfi
Feb 8, 2008·Trends in Ecology & Evolution·Max Rietkerk, Johan van de Koppel
Jun 14, 2008·Journal of Theoretical Biology·Alon Manor, Nadav M Shnerb
May 14, 2009·Physical Review Letters·Alon Manor, Nadav M Shnerb
Aug 5, 2009·Journal of Theoretical Biology·René LefeverOlivier Lejeune
Feb 6, 2010·Proceedings. Biological Sciences·Jost von HardenbergEhud Meron

Related Concepts

In Silico
Fluctuation
Stochastic Processes
Anatomic Bifurcation
Sustain
Nature
Symmetry
Disintegration (Morphologic Abnormality)
Habitat
Pattern Formation

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