Asymptotic analysis of Complex Automata models for reaction-diffusion systems

• Autores: Alfonso Caiazzo, Jean-Luc Falcone, Bastien Chopard, Alfons G. Hoekstra
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 59, Nº. 8, 2009, págs. 2023-2034
• Idioma: inglés
• DOI: 10.1016/j.apnum.2009.04.001
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• Resumen

  • Complex Automata (CxA) have been recently introduced as a paradigm to simulate multiscale multiscience systems as a collection of generalized Cellular Automata on different scales. The approach yields numerical and computational challenges and can become a powerful tool for the simulation of particular complex systems. We present a mathematical framework for CxA modeling to investigate the behavior of the model depending on scale separation and modeling choices. For a simple CxA model for a reaction�diffusion process, we define a Complex Automata model, deriving theoretical error estimates, which are numerically validated.