  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.
