Control Global Loops in Self-Organizing Systems

Self-organizing systems are used to model complex or at least apparent complex behaviors. The idea currently in use is to study global behaviors based only on fixed and local rules. The emergence of a specific global behavior depends too strongly on the initial state of the system. This chaotic aspect can be avoided adding, besides the local loops, a global control loop to balance the too big "local freedom". The global loop can be used to tune the local behavior so as the entire system becomes more stable. Using various reduction functions some global parameters are extracted from the system and sent back locally to the elements of the system. The information received locally through the global loop is used to "tune" the local behavior. So the self-organized system becomes "less self-organized", but more flexible in maintaining its global state in prescribed limits. In order to illustrate the idea, the paper presents simple examples of cellular automata with global loops.