Journal
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
Volume 97, Issue 18, Pages 9840-9843Publisher
NATL ACAD SCIENCES
DOI: 10.1073/pnas.97.18.9840
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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.
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