1996/05/31 by Cyrill B. Muratov, C. B. Muratov · 2 citations
Computer Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Nonlinear Dynamics and Pattern Formation #Theoretical and Computational Physics #nlin.PS #patt-sol
paper · pdf · doi:10.1103/physreve.54.3369
published as Phys. Rev. E 54, 3369 (1996). · 9 pages (ReVTeX), 5 figures (postscript). To be published in Phys. Rev. E
arxiv created 1996/06/24 · openalex publication_date 1996/10/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
An asymptotic equation of motion for the pattern interface in the domain-forming reaction-diffusion systems is derived. The free boundary problem is reduced to the universal equation of nonlocal contour dynamics in two dimensions in the parameter region where a pattern is not far from the points of the transverse instabilities of its walls. The contour dynamics is studied numerically for the reaction-diffusion system of the FitzHugh-Nagumo type. It is shown that in the asymptotic limit the transverse instability of the localized domains leads to their splitting and formation of the multidomain pattern rather than fingering and formation of the labyrinthine pattern. \textcopyright 1996 The American Physical Society.