Network-theory based modeling of avalanche dynamics in percolative tunnelling networks

Brain-like self-assembled networks can infer and analyze information out of unorganized noisy signals with minimal power consumption. These networks are characterized by spatiotemporal avalanches and their crackling behavior, and their physical models are expected to predict and understand their computational capabilities. Here, we use a network theory-based approach to provide a physical model for percolative tunnelling networks, found in Ag-hBN system, consisting of nodes (atomic clusters) of Ag intercalated in the hBN van der Waals layers. By modeling a single edge plasticity through constitutive electrochemical filament formation, and annihilation through Joule heating, we identify independent parameters that determine the network connectivity. We construct a phase diagram and show that a small region of the parameter space contains signals which are long-range temporally correlated, and only a subset of them contains crackling avalanche dynamics. Physical systems spontaneously selforganize to this region for possibly maximizing the efficiency of information transfer.