Research Describes Synchronization of Chaotic Systems

Research Describes Synchronization of Chaotic Systems

Researchers from Bar-Ilan University analyzed the Rossler system and measured the fine grain process that leads from disorder to synchrony

A team of researchers from Bar-Ilan University, Universidad Rey Juan Carlos, Universidad Politécnica de Madrid, Indian Statistical Institute, CNR-Institute of Complex Systems, and Northwestern Polytechnical University analyzed the Rossler system—a chaotic system. The team was able to measure the fine grain process that leads from disorder to synchrony and found a new kind of synchronization between chaotic systems, dubbed as ‘Topological Synchronization’. In conventional process, synchronization is examined by comparing the time-course of activity of the two systems. However, topological synchronization examines synchronization by comparing the structures of the systems. Therefore, chaotic system is examined at the level of its structure with the help of a more global approach to determine the process of synchronization.

According to Nir Lahav, of Bar-Ilan University’s Department of Physics, the study’s lead author, although chaotic systems are unpredictable, they have a subtle global organization called strange attractor. Each chaotic system attracts its own unique strange attractor. In topological synchronization, two strange attractors have the same organization and structures. In the initial phase of the synchronization process, small areas on one strange attractor have the same structure of the other attractor. This suggests that the small areas are already synced to the other attractor. In the final stage, all the areas of one strange attractor are expected to have the structure of the other and complete topological synchronization is reached.

The findings reveal that chaotic systems synchronize gradually through local structures that emerge in the sparse areas of the system and later spread to the more populated areas. The activity is less chaotic in these sparse areas compared to other areas. Therefore, it is easier for these areas to sync relative to those that are highly erratic. The researchers stated that the conceptual novelty pertains fundamental understanding of synchronization and has direct practical implications on the predictability limits of chaotic systems. Moreover, the researchers demonstrated that the state of one system can be inferred from measurements of the other, even when global synchrony is not present, using this newly-defined local synchronization. The research was published in the journal Physical Review E on November 06, 2018.