Cellular Automata (CA) are a class of discrete dynamical systems that havebeen widely used to model complex systems in which the dynamics is specified atlocal cell-scale. Classically, CA are run on a regular lattice and with perfectsynchronicity. However, these two assumptions have little chance to truthfullyrepresent what happens at the microscopic scale for physical, biological orsocial systems. One may thus wonder whether CA do keep their behavior whensubmitted to small perturbations of synchronicity. This work focuses on the study of one-dimensional (1D) asynchronous CA withtwo states and nearest-neighbors. We define what we mean by ``the behavior ofCA is robust to asynchronism'' using a statistical approach with macroscopicparameters. and we present an experimental protocol aimed at finding which arethe robust 1D elementary CA. To conclude, we examine how the results exposedcan be used as a guideline for the research of suitable models according torobustness criteria.
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