Asymptotic analysis of Complex Automata models for reaction–diffusion systems

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.