TY - JOUR
T1 - Scaling laws and the prediction of bifurcations in systems modeling pattern formation
AU - Scovel, Clint
AU - Kevrekids, Ioannis G.
AU - Nicolaenko, Basil
N1 - Funding Information:
We are happy to acknowledget hat this-work was prompted by Professor Chris Eilbeck’s comment during a CNLS seminar that “there has to be some way of predicting when the unimodal branch hits the bimodal branch”. A discussion of Michael Weinstein with one of us (IGK) was also helpful in clearing up some of the proofs. We also thank Mr. Harry S. Brown for his computational assistancei n the preparation of fig. 1. This work was supported in part by NSF Grants no. CBT-8707090 and EET-87 17787t o I.G. Kevrekidis. We acknowledget he support of the U.S. Department of Energy through the hospitality of the Center for Nonlinear Studies at Los Alamos.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 1988/6/27
Y1 - 1988/6/27
N2 - When the typical pattern size is used as a bifurcation parameter, partial differential equations modeling pattern formation possess a scaling law. We exploit this scaling law in the prediction of the complex bifurcation structure typically observed in such systems. The Kuramoto-Sivashinsky equation with periodic boundary conditions is used as an illustrative example.
AB - When the typical pattern size is used as a bifurcation parameter, partial differential equations modeling pattern formation possess a scaling law. We exploit this scaling law in the prediction of the complex bifurcation structure typically observed in such systems. The Kuramoto-Sivashinsky equation with periodic boundary conditions is used as an illustrative example.
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U2 - 10.1016/0375-9601(88)90242-3
DO - 10.1016/0375-9601(88)90242-3
M3 - Article
AN - SCOPUS:0007430071
SN - 0375-9601
VL - 130
SP - 73
EP - 80
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 2
ER -