Synchronization in chaotic systems with artificial neural networks

Chaos is the apparently irregular motion that is, in reality, nonlinear but deterministic. Chaos exhibits extremely sensitive dependence on initial conditions; this tends to prevent the prediction the behavior of a chaotic system. It has been demonstrated, however, that chaotic systems can be synchronized by linking them with common driving signals. This study proposes a methodology for synchronizing chaos by resorting to artificial neural networks (ANN´s). The ANN´s are capable of approximately learning the chaotic behavior, and, thus, they render possible the synchronization of systems whose deterministic governing equations are not sufficiently well known. This requires training them with experimentally obtained time-series data and the aid of common driving signals. Examples are given for two iterated maps