  Simple dynamical models can produce intricate behaviors in large networks.
These behaviors can often be observed in a wide variety of physical systems
captured by the network of interactions. Here we describe a phenomenon where
the increase of dimensions self-consistently generates a force field due to
dynamical instabilities. This can be understood as an unstable ("rumbling")
tunneling mechanism between minima in an effective potential. We dub this
collective and nonperturbative effect a "Lyapunov force" which steers the
system towards the global minimum of the potential function, even if the full
system has a constellation of equilibrium points growing exponentially with the
system size. The system we study has a simple mapping to a flow network,
equivalent to current-driven memristors. The mechanism is appealing for its
physical relevance in nanoscale physics, and to possible applications in
optimization, novel Monte Carlo schemes and machine learning.
