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A complex syntony: driving chimera states networks with external stochastic signals

A complex syntony: driving chimera states networks with external stochastic signals
A new framework for analysing the effect of the external environment on single-layer chimera state networks by driving the system with random external univariate and multivariate signals

Chimera states are a intriguing phenomenon in which the identical oscillators in a network segregate into two different groups: a high-coherence group and a low-coherence group, thus howing a spontaneous breaking of the system’s simmetry. Moreover, it is known that chimera states networks are powerful representations of real-world complex systems, such as the brain, where both the complete synchronization and the complete desynchronization of the components would not allow a correct functioning of the system. Hence, the partial synchronization observed in such states is highly desired.

In this context, the interactions between different networks of chimera states have been extensively studied in multi-layer systems, due to the importance of synchronization phenomena not only within layers but also across layers of the same network. At the same time a comprehensive understanding of the environment’s synchronizing effects on chimera state networks is still missing. In this project we propose a new framework for analysing the effect of the external environment on single-layer chimera state networks by driving the system with random external univariate and multivariate signals. While the chimera state collapse to a fully synchronized state in finite un-driven networks is a well-known phenomenon, we also observe an increase of collapses when the network is driven by external signals. For this reason, we use quantities in order to measure the mean-life time of chimera states and the external driving’ synchronizing power in function of the system’s parameters: the coupling strength, the signal’s variance and the magnitude of the autocorrelation. This new framework and the information gleaned by driving the network with stochastic signals provide the foundations for being able to drive the network with more complex and realistic signals such as EEGs. Indeed, the synchronisation-desynchronisation mechanisms observed in chimera states can be found in the brains of epilepsy patients, thus estabilishing a bridge between these intriguing phenomena and one of the world’s most common neurological disorders. The reason behind using the EEGs as a driver is that we expect the driven layer to synchronize with the signal; the degree of synchronizability will depend on the particular EEG used, allowing us to explore the different effects that EEG signals have on the driven layer in relation to where they were recorded in the brain. By correlating the synchronization power to the area of the brain in which the EEGs were recorded, we thus expect to be able to localize the seizure-generating area of the brain. As it is known, this is of crucial importance for all those patients who cannot manage their conditions via medication, but must go under surgical operation to resect the area of the brain which causes the seizures.

Principal researchers

Ralph Andrzejak

Researchers

Jacopo Epifanio