| Abstract: |
| Given two unidirectionally coupled nonlinear systems, we speak of generalized synchronization when the responder "follows" the driver. Mathematically, this situation is implemented by a map from the driver state space to the responder state space termed the synchronization map. In nonlinear times series analysis, the framework of this communication, the existence of the synchronization map amounts to the invertibility of the so-called cross map, which is a continuous map that exists in the reconstructed state spaces for typical time-delay embeddings. The cross map plays a central role in some techniques to detect functional dependencies between time series. In this communication, we will discuss only the noiseless scenario, i.e., when noise is not present in the driver. To reveal generalized synchronization, we check the existence of synchronization maps using recurrent neural networks and predictability. The results demonstrate the capability of our method. |
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