Transient behavior in systems with time-delayed feedback

Anatomical connectivity influences both intra- and inter-brain synchronizations

Recent development in diffusion spectrum brain imaging combined to functional simulation has the potential to further our understanding of how structure and dynamics are intertwined in the human brain. At the intra-individual scale, neurocomputational models have already started to uncover how the human connectome constrains the coordination of brain activity across distributed brain regions. In parallel, at the inter-individual scale, nascent social neuroscience provides a new dynamical vista of the coupling between two embodied cognitive agents. Using EEG hyperscanning to record simultaneously the brain activities of subjects during their ongoing interaction, we have previously demonstrated that behavioral synchrony correlates with the emergence of inter-brain synchronization. However, the functional meaning of such synchronization remains to be specified. Here, we use a biophysical model to quantify to what extent inter-brain synchronizations are related to the anatomical and functional similarity of the two brains in interaction. Pairs of interacting brains were numerically simulated and compared to real data. Results show a potential dynamical property of the human connectome to facilitate inter-individual synchronizations and thus may partly account for our propensity to generate dynamical couplings with others.

Adaptive tuning of feedback gain in time-delayed feedback control

We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback gain. This adaptive controller is applied to the stabilization of an unstable fixed point and an unstable periodic orbit embedded in a chaotic attractor. The adaptation algorithm is constructed using the speed-gradient method of control theory. Our computer simulations show that the adaptation algorithm can find an appropriate value of the feedback gain for single and multiple delays. Furthermore, we show that our method is robust to noise and different initial conditions.