@article{38481,
  keywords = {models, connffessit},
  author = {Theodoropoulos and Qian and Kevrekidis},
  title = {"Coarse" stability and bifurcation analysis using time-steppers: A reaction-diffusion example},
  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. },
  year = {2000},
  journal = {Proceedings of the National Academy of Sciences of the United States of AmericaProceedings of the National Academy of Sciences of the United States of America},
  volume = {97},
  pages = {9840-9843},
  month = {08/2000},
  isbn = {0027-8424},
  language = {English},
}