"Coarse" stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Constantinos Theodoropoulos, Yue Hong Qian, Ioannis G. Kevrekidis

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183 Scopus citations

Abstract

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099-1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective ("coarse") bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice-Boltzmann model.

Original languageEnglish (US)
Pages (from-to)9840-9843
Number of pages4
JournalProceedings of the National Academy of Sciences of the United States of America
Volume97
Issue number18
DOIs
StatePublished - Aug 29 2000

All Science Journal Classification (ASJC) codes

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