Redundant and synergistic interactions in a complex network of single-transistor electronic chaotic oscillators and...

Complex networks often exhibit emergent behaviors, where simple dyadic interactions yield collective dynamics that cannot be explained by examining the system's units individually or in pairs. Understanding how redundant and synergistic interaction emerges from elementary connectivity patterns is important in characterizing the behavior of physical, biological, and engineering systems. In this study, the information-theoretic framework of Partial Information Decomposition (PID) is employed to investigate how pairs of signals measured at the nodes of large network systems contribute individually and jointly to determine the overall state of the network. The analyzed systems are networks of numerically simulated Rössler oscillators and physical single-transistor electronic chaotic oscillators, reproducing purely pairwise and symmetric links in biological neuronal cultures, and cortical electroencephalographic networks assessed in humans. In the two settings, PID was extensively applied to decompose the information brought by pairs of signals to the overall state of the system, which was assessed respectively as the dynamic regime (from asynchronous chaos to synchronization) and the subject condition (open vs closed eyes). Our approach highlights the coexistence of redundant and synergistic interplays in determining the effect of the pairwise dynamics on the system's state. Specifically, we demonstrate how, in a highly synchronized system, where units act following overlapped redundant behaviors, their joint consideration helps determine the system's state though their synergistic interactions. Our findings reveal the emergence of non-trivial behaviors in networked systems based on pairwise connections and straightforward neural states, highlighting the need for using appropriate analytical tools to capture complex phenomena.