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Understanding statistical properties of cognitive systems is one of the main goal of complex systems physics. The automata gas is a statistical system whose particles perform information based interactions and use a decision mechanism. The collective nature of such interactions is at the base of the self-organized dynamical states of the system. In some cases it is possible to study the emergence of these states, by using an adiabatic separation between the single particle time scale and the particle distribution time scale. Then the emergent properties can be related to the solutions of a nonlinear diĀ®usion equation. The considered models have a wide range of application in biology and social sciences to describe the self-organization properties observed in the experiments. Our main interest is to develop a model for the pedestrian dynamics in a urban space. We study the properties of a automata gas in some simple cases and we discuss the comparison with experimental data.
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