Experimental synchronization between neuroelectrical activity and an elementary electronic chaotic oscillator

Abstract

The synchronization between structurally heterogeneous dynamical systems remains a relatively underinvestigated area in nonlinear systems, particularly in the context of experimental studies. The present work demonstrates real-time analog-domain synchronization between human electroencephalographic (EEG) signals and an electronic chaotic oscillator realized using a single transistor. The EEG signals were directly coupled to the oscillator circuit according to the master–slave scheme. Through experimental investigation, it was found that strong phase locking could be achieved despite the profound differences in their origin, spectral, and dynamical features. While exhibiting a level of entrainment that could be detected both as phase locking and directed information transfer, the dynamics of the electronic oscillator remained partially independent of the external stimulus, namely, the filtered EEG. In turn, this allowed the generation of complex responses to the external disturbance, which essentially acted as a generator of new linear features, as visible on the time-frequency spectrograms. In the absence of disturbance, the chaotic oscillator generated a signal with strong deterministic features revealed by the convergence of the correlation dimension curves. Although the external perturbation partially disrupted the structure, it was found that the oscillator preferentially synchronized with the measured EEG signal compared to its amplitude-adjusted phase-scrambled surrogate. In addition, state transitions in the chaotic oscillator dynamically matched changes in brain states (e.g., eyes-open versus eyes-closed). A circuit board integrating the entire signal flow from the electrode to the chaotic oscillator was realized. On the one hand, these results provide new experimental evidence of the ability of low-dimensional chaotic systems to react to and partially synchronize with highly complex external inputs. On the other hand, this work opens up possibilities for future analog hybrid systems in which the brain and machine are integrated seamlessly through continuous dynamical coupling.