Symbolic Dynamical Characterization for Multistability in Remote Synchronization Phenomena

Abstract

Two of the most remarkable phenomena in non-linear systems are multistability and remote synchronization. In the first one, depending on the initial conditions, the system may set in different states after the transient, while in the other, dynamical units that are not directly connected set in a synchronized state. In this work, we introduce a new approach to detect multistability in the remote synchronization phenomena where the dynamical system is given by a star-like topology whose oscillators are governed by the Stuart-Landau equation. This approach is based on symbolic dynamics characterization and complex network formalism. It has already been used to detect periodic windows and chaos in non-linear systems and now we show that although it is not able to differ from a non-synchronized to a synchronized state, it is able to detect the region where multistability takes place. Our findings are compared with the results obtained by traditional methods such as the partial synchronization index.