@article{133085d5d01446dd87b439564e78b679,
title = "Scaling laws and the prediction of bifurcations in systems modeling pattern formation",
abstract = "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.",
author = "Clint Scovel and Kevrekids, {Ioannis G.} and Basil Nicolaenko",
note = "Funding Information: We are happy to acknowledget hat this-work was prompted by Professor Chris Eilbeck{\textquoteright}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.",
year = "1988",
month = jun,
day = "27",
doi = "10.1016/0375-9601(88)90242-3",
language = "English (US)",
volume = "130",
pages = "73--80",
journal = "Physics Letters A",
issn = "0375-9601",
publisher = "Elsevier B.V.",
number = "2",
}