Synchronization, Control and Data Assimilation of the Lorenz System

We explore several aspects of replica synchronization with the goal of retrieving the values of parameters applied to the Lorenz system. The idea is to establish a computer replica (slave) of a natural system (master, simulated in this paper), and exploit the fact that the slave synchronizes with the master only if they evolve with the same parameters. As a byproduct, in the synchronized phase, the state variables of the slave and those of the master are the same, thus allowing us to perform measurements that would be impossible in the real system. We review some aspects of master-slave synchronization using a subset of variables with intermittent coupling. We show how synchronization can be achieved when some of the state variables are available for direct measurement using a simulated annealing approach, and also when they are accessible only through a scalar function, using a pruned-enriching ensemble approach, similar to genetic algorithms without cross-over. We also explore the case of exploiting the "gene exchange" option among members of the ensemble.