TY - JOUR
T1 - Giant Amplification of Noise in Fluctuation-Induced Pattern Formation
AU - Biancalani, Tommaso
AU - Jafarpour, Farshid
AU - Goldenfeld, Nigel
N1 - Publisher Copyright:
© 2017 American Physical Society.
PY - 2017/1/3
Y1 - 2017/1/3
N2 - The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and nonorthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, when driven by the ever-present intrinsic noise, lead to persistent large amplitude patterns. This mechanism shows that fluctuation-induced Turing patterns are observable, and are not strongly limited by the amplitude of demographic stochasticity nor by the value of the diffusion coefficients.
AB - The amplitude of fluctuation-induced patterns might be expected to be proportional to the strength of the driving noise, suggesting that such patterns would be difficult to observe in nature. Here, we show that a large class of spatially extended dynamical systems driven by intrinsic noise can exhibit giant amplification, yielding patterns whose amplitude is comparable to that of deterministic Turing instabilities. The giant amplification results from the interplay between noise and nonorthogonal eigenvectors of the linear stability matrix, yielding transients that grow with time, and which, when driven by the ever-present intrinsic noise, lead to persistent large amplitude patterns. This mechanism shows that fluctuation-induced Turing patterns are observable, and are not strongly limited by the amplitude of demographic stochasticity nor by the value of the diffusion coefficients.
UR - http://www.scopus.com/inward/record.url?scp=85009458350&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85009458350&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.118.018101
DO - 10.1103/PhysRevLett.118.018101
M3 - Article
C2 - 28106453
AN - SCOPUS:85009458350
SN - 0031-9007
VL - 118
JO - Physical review letters
JF - Physical review letters
IS - 1
M1 - 018101
ER -