Turing patterns and Newell—Whitehead—Segel amplitude equation

Two-dimensional (2D) reaction—diffusion systems with linear and nonlinear diffusion terms are examined for their behavior when a Turing instability arises and stationary spatial patterns form. It is shown that a 2D nonlinear analysis for striped patterns leads to the Newell—Whitehead—Segel amplitude equation in which the contribution from spatial derivatives depends only on the linearized diffusion term of the original model. In the absence of this contribution, i.e., for the normal forms, standard methods are used to calculate the coefficients of the equation.

PACS: 05.45.−a, 47.54.−r, 82.40.Bj, 82.40.Ck (all)
DOI: 10.3367/UFNe.0184.201410j.1149
URL: https://ufn.ru/en/articles/2014/10/f/
Web of Science

000346960100002
Scopus

2-s2.0-84920033426
ADS NASA

2014PhyU...57.1035Z
Citation: Zemskov E P "Turing patterns and Newell—Whitehead—Segel amplitude equation" Phys. Usp. 57 1035–1037 (2014)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 25th, December 2013, revised: 11th, February 2014, accepted: 11th, February 2014

Оригинал: Земсков Е П «Тьюринговы структуры и амплитудное уравнение Ньюэлла—Уайтхеда—Сегела» УФН 184 1149–1151 (2014); DOI: 10.3367/UFNr.0184.201410j.1149

References (18) Cited by (3) Similar articles (16) ↓

A.I. Lavrova, E.B. Postnikov, Yu.M. Romanovsky “Brusselator: an abstract chemical reaction?” Phys. Usp. 52 1239–1244 (2009)
O.V. Rudenko “Nonlinear dynamics of quadratically cubic systems” Phys. Usp. 56 683–690 (2013)
Yu.L. Klimontovich “What are stochastic filtering and stochastic resonance?” Phys. Usp. 42 37–44 (1999)
S.N. Gordienko “Irreversibility and the probabilistic treatment of the dynamics of classical particles” Phys. Usp. 42 573–590 (1999)
P.S. Landa, Ya.B. Duboshinskii “Self-oscillatory systems with high-frequency energy sources” Sov. Phys. Usp. 32 723–731 (1989)
E.N. Rumanov “Critical phenomena far from equilibrium” Phys. Usp. 56 93–102 (2013)
V.I. Klyatskin “Statistical topography and Lyapunov exponents in stochastic dynamical systems” Phys. Usp. 51 395–407 (2008)
V.V. Brazhkin “Why does statistical mechanics 'work' in condensed matter?” Phys. Usp. 64 1049–1057 (2021)
A.V. Borisov, A.O. Kazakov, S.P. Kuznetsov “Nonlinear dynamics of the rattleback: a nonholonomic model” Phys. Usp. 57 453–460 (2014)
A.N. Pavlov, V.S. Anishchenko “Multifractal analysis of complex signals” Phys. Usp. 50 819–834 (2007)
A. Loskutov “Dynamical chaos: systems of classical mechanics” Phys. Usp. 50 939–964 (2007)
A.V. Borisov, I.S. Mamaev “Strange attractors in rattleback dynamics” Phys. Usp. 46 393–403 (2003)
V.Yu. Shishkov, E.S. Andrianov et al “Relaxation of interacting open quantum systems” Phys. Usp. 62 510–523 (2019)
N.V. Selina “Light diffraction in a plane-parallel layered structure with the parameters of a Pendry lens” Phys. Usp. 65 406–414 (2022)
G.S. Golitsyn “A N Kolmogorov's 1934 paper is the basis for explaining the statistics of natural phenomena of the macrocosm” Phys. Usp. 67 80–90 (2024)
V.S. Vavilov, P.C. Euthymiou, G.E. Zardas “Persistent photoconductivity in semiconducting III-V compounds” Phys. Usp. 42 199–201 (1999)

The list is formed automatically.