CHAOS, SYNCHRONIZATION AND CONTROL IN CELLULAR AUTOMATA

We investigate the mechanism of pinching synchronization (complete synchronization for a fraction of system) for cellular automata, consid- ered as prototypes of discrete systems with unpredictable behaviour (finite- distance chaoticity). The pinching synchronization threshold is related to this chaoticity. Some control problems may be reformulated as targeted synchronization. In these problems one aims at discovering a protocol that keeps the distance between two replicas below a certain threshold with the minimum effort, given some constraints. We have chosen to investigate the behaviour of two control schemes based on the local number of non-zero first-order derivatives, taking as reference the “blind” pinching synchroniza- tion protocol. We have shown that, differently from usual chaotic systems, one can exploit self-annihilation of defects to obtain synchronization with a weaker control.