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PubMed · 10963656

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

C Theodoropoulos·Y H Qian·I G Kevrekidis
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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.

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Computer SimulationKineticsMathematicsModels, TheoreticalJournal ArticleResearch Support, Non-U.S. Gov'tResearch Support, U.S. Gov't, Non-P.H.S.

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C Theodoropoulos, Y H Qian, I G Kevrekidis. 2000-08-29. "Coarse" stability and bifurcation analysis using time-steppers: a reaction-diffusion example.. https://doi.org/10.1073/pnas.97.18.9840

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