Synchronization of chaotic systems and long short-term memory networks by sharing a single variable

Abstract

We adopt long short-term memory (LSTM) networks to model and characterize chaotic systems rather than conventional dynamical equations. We find that a well-trained LSTM system can synchronize with its learned chaotic system via transmitting a common signal. In the same fashion, we show that when learning an identical chaotic system, the trained LSTM systems can also be synchronized. Remarkably, we find that a cascading synchronization will be achieved among chaotic systems and their trained LSTM systems in the same manner. We further validate that this synchronization behavior is robust even the transmitting signal is contaminated with relatively a high level of white noise. Our work reveals that synchronization is a common behavior linking chaotic systems and their learned LSTM networks.